diff --git a/firedrake/adjoint/transformed_functional.py b/firedrake/adjoint/transformed_functional.py
index d3eeb2f46b..ce739edf4d 100644
--- a/firedrake/adjoint/transformed_functional.py
+++ b/firedrake/adjoint/transformed_functional.py
@@ -176,28 +176,6 @@ def is_dg_space(space: WithGeometry) -> bool:
     return e.is_dg()
 
 
-def dg_space(space: WithGeometry) -> WithGeometry:
-    """Construct a DG space containing a given function space as a subspace.
-
-    Parameters
-    ----------
-
-    space
-        A function space.
-
-    Returns
-    -------
-
-    firedrake.functionspaceimpl.WithGeometry
-        A DG space containing `space` as a subspace. May be `space`.
-    """
-
-    if is_dg_space(space):
-        return space
-    else:
-        return fd.FunctionSpace(space.mesh(), finat.ufl.BrokenElement(space.ufl_element()))
-
-
 class L2TransformedFunctional(AbstractReducedFunctional):
     r"""Represents the functional
 
@@ -265,7 +243,8 @@ def __init__(self, functional: pyadjoint.OverloadedType, controls: Union[Control
         self._space_D = Enlist(space_D)
         if len(self._space_D) != len(self._space):
             raise ValueError("Invalid length")
-        self._space_D = tuple(dg_space(space) if space_D is None else space_D
+        self._space_D = tuple((space if is_dg_space(space) else space.broken_space())
+                              if space_D is None else space_D
                               for space, space_D in zip(self._space, self._space_D))
 
         self._controls = tuple(Control(fd.Function(space_D), riesz_map="l2")
diff --git a/firedrake/functionspaceimpl.py b/firedrake/functionspaceimpl.py
index 5b8d6b44a1..926824345f 100644
--- a/firedrake/functionspaceimpl.py
+++ b/firedrake/functionspaceimpl.py
@@ -403,6 +403,19 @@ def make_function_space(cls, mesh, element, name=None):
             new = cls.create(new, mesh)
         return new
 
+    def broken_space(self):
+        """Return a :class:`.WithGeometryBase` with a :class:`finat.ufl.BrokenElement`
+        constructed from this function space's FiniteElement.
+
+        Returns
+        -------
+        WithGeometryBase :
+            The new function space with a :class:`~finat.ufl.BrokenElement`.
+        """
+        return type(self).make_function_space(
+            self.mesh(), finat.ufl.BrokenElement(self.ufl_element()),
+            name=f"{self.name}_broken" if self.name else None)
+
     def reconstruct(
         self,
         mesh: MeshGeometry | None = None,
diff --git a/firedrake/slate/static_condensation/hybridization.py b/firedrake/slate/static_condensation/hybridization.py
index cfc72f2119..e66c4c547f 100644
--- a/firedrake/slate/static_condensation/hybridization.py
+++ b/firedrake/slate/static_condensation/hybridization.py
@@ -1,7 +1,6 @@
 import functools
 
 import ufl
-import finat.ufl
 
 import firedrake.dmhooks as dmhooks
 from firedrake.slate.static_condensation.sc_base import SCBase
@@ -90,8 +89,7 @@ def initialize(self, pc):
         TraceSpace = FunctionSpace(mesh[self.vidx], "HDiv Trace", tdegree)
 
         # Break the function spaces and define fully discontinuous spaces
-        broken_elements = finat.ufl.MixedElement([finat.ufl.BrokenElement(Vi.ufl_element()) for Vi in V])
-        V_d = FunctionSpace(mesh, broken_elements)
+        V_d = V.broken_space()
 
         # Set up the functions for the original, hybridized
         # and schur complement systems
diff --git a/tests/firedrake/regression/test_function_spaces.py b/tests/firedrake/regression/test_function_spaces.py
index ab22b66ddb..491354df19 100644
--- a/tests/firedrake/regression/test_function_spaces.py
+++ b/tests/firedrake/regression/test_function_spaces.py
@@ -120,7 +120,7 @@ def test_function_space_variant(mesh, space):
 
 
 @pytest.mark.parametrize("modifier",
-                         [BrokenElement, HDivElement,
+                         [HDivElement,
                           HCurlElement])
 @pytest.mark.parametrize("element",
                          [FiniteElement("CG", triangle, 1),
@@ -313,3 +313,46 @@ def test_reconstruct_sub_component(dg0, rt1, mesh, mesh2, dual):
             assert is_primal(V1.parent) == is_primal(V2.parent) != dual
             assert V1.parent.ufl_element() == V2.parent.ufl_element()
             assert V1.parent.index == V2.parent.index == index
+
+
+@pytest.mark.parametrize("family", ("CG", "BDM", "DG"))
+@pytest.mark.parametrize("shape", (0, 2, (2, 3)), ids=("0", "2", "(2,3)"))
+def test_broken_space(mesh, shape, family):
+    """Check that FunctionSpace.broken_space returns the a
+    FunctionSpace with the correct element.
+    """
+    kwargs = {"variant": "spectral"} if family == "DG" else {}
+
+    elem = FiniteElement(family, mesh.ufl_cell(), 1, **kwargs)
+
+    if not isinstance(shape, int):
+        make_element = lambda elem: TensorElement(elem, shape=shape)
+    elif shape > 0:
+        make_element = lambda elem: VectorElement(elem, dim=shape)
+    else:
+        make_element = lambda elem: elem
+
+    fs = FunctionSpace(mesh, make_element(elem))
+    broken = fs.broken_space()
+    expected = FunctionSpace(mesh, make_element(BrokenElement(elem)))
+
+    assert broken == expected
+
+
+def test_mixed_broken_space(mesh):
+    """Check that MixedFunctionSpace.broken_space returns the a
+    MixedFunctionSpace with the correct element.
+    """
+
+    mixed_elem = MixedElement([
+        FiniteElement("CG", mesh.ufl_cell(), 1),
+        VectorElement("BDM", mesh.ufl_cell(), 2, dim=2),
+        TensorElement("DG", mesh.ufl_cell(), 1, shape=(2, 3), variant="spectral")
+    ])
+    broken_elem = MixedElement([BrokenElement(elem) for elem in mixed_elem.sub_elements])
+
+    mfs = FunctionSpace(mesh, mixed_elem)
+    broken = mfs.broken_space()
+    expected = FunctionSpace(mesh, broken_elem)
+
+    assert broken == expected