Preheat oven to 550 degrees F° with baking steel or pizza stone inside the oven for 1 hour.
MAKE CHEESE SAUCE: Melt butter in a pot on medium heat. Add flour and whisk constantly for 30 seconds. Add milk and whisk well. Add cheddar cheese, mix. Add salt and pepper, mix. Reduce heat to low when it starts to boil. Cook until cheese reaches desired consistency, whisking often.
Grate mozzarella cheese. Chop broccoli, then steam for 3 minutes.
Flour surface and roll out the dough. Put a floured pizza peel underneath the dough. Add cheese sauce, mozzarella and broccoli, then pat down toppings. Drizzle a little more cheese sauce on top of the broccoli.
Bake pizza in the oven at 550 degrees F° for 8-10 minutes.
Remove pizza from oven with pizza peel and let cool for 5 minutes.