Add an inch of water to a large saucepan. Place a steamer basket in the pot. Bring water to a boil and add the broccoli. Cover and steam for 4 to 5 minutes.
While broccoli is cooking, melt butter in a medium saucepan. Add flour and cook and stir for 1 minute.
Whisk in milk and bring to a simmer.
Turn eat to low and stir in salt, pepper, Parmesan cheese, and cheddar cheese. Stir until cheese is melted. Add more milk if too thick. Remove from heat.