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