Place a steamer insert into a saucepan and fill with water to just below the bottom of the insert. Bring the water to a boil.
Add the broccoli, cover the pot, and steam the broccoli until fork-tender, 8 to 10 minutes.
Transfer broccoli to a blender and allow to cool slightly, about 5 minutes.
Place milk, Cheddar cheese, and Parmesan cheese in the blender. Carefully start the blender, using a few quick pulses to get the mixture moving before leaving it on to puree. Alternately, you can use a stick blender and puree in a bowl.
