Heat oven to 375°F; butter a 2-quart dish. Boil broccoli 2 minutes; drain and spread on a towel to release excess water.
Melt 3 tablespoons butter in a saucepan over medium heat. Whisk in flour 1 minute; gradually add milk and broth.
Simmer 3 to 4 minutes until sauce coats a spoon. Remove from heat; stir in mustard, salt, pepper, and cheddar until smooth.
Fold broccoli into sauce; transfer to dish. Toss cracker crumbs with topping butter; scatter over surface.
Bake 20 to 25 minutes until edges bubble and top is golden. Rest 5 minutes before serving.