Best Broccoli Gratin

¼ c. butter, plus extra to grease baking dish3 T. flour1 ½ c. milkSalt, fresh black pepper, to tastePinch grated nutmeg8 c. fresh broccoli, cut into small florets (about 4 heads)1 c. grated sharp cheddar cheese½ c. seasoned bread crumbsPaprika…