diff --git a/docker/python-builder/scripts/assemble b/docker/python-builder/scripts/assemble
index 28907a0511..4d9aa0eb83 100755
--- a/docker/python-builder/scripts/assemble
+++ b/docker/python-builder/scripts/assemble
@@ -44,14 +44,15 @@ function install_wheels {
     # Build a wheel so that we have an install target.
     # pip install . in the container context with the mounted
     # source dir gets ... exciting.
-    # We run sdist first to trigger code generation steps such
-    # as are found in zuul, since the sequencing otherwise
-    # happens in a way that makes wheel content copying unhappy.
-    # pip wheel isn't used here because it puts all of the output
+    # The `build` tool builds an sdist first then a wheel from
+    # that sdist which is exactly what we want. This triggers code
+    # generation steps such as are found in zuul, since the sequencing
+    # otherwise happens in a way that makes wheel content copying unhappy.
+    # `pip wheel` isn't used here because it puts all of the output
     # in the output dir and not the wheel cache, so it's not
     # possible to tell what is the wheel for the project and
     # what is the wheel cache.
-    python3 setup.py sdist bdist_wheel -d /output/wheels
+    /tmp/venv/bin/python3 -m build -o /output/wheels ./
 
     # Install everything so that the wheel cache is populated with
     # transitive depends. If a requirements.txt file exists, install
@@ -88,7 +89,7 @@ done
 # Use a clean virtualenv for install steps to prevent things from the
 # current environment making us not build a wheel.
 python3 -m venv /tmp/venv
-/tmp/venv/bin/pip install -U pip wheel
+/tmp/venv/bin/pip install -U pip wheel build
 
 # If there is an upper-constraints.txt file in the source tree,
 # use it in the pip commands.