Preheat oven to 350°F.

Melt 2 tablespoons of butter in medium saucepan over medium high heat. 

Add in onions and cook until translucent, about 4 minutes. 

 Stir in flour and stir to coat onions. Cook for 2 minutes.

Remove from heat and whisk in hot milk. Return to heat and bring to a simmer.

Stir in cheese by the handful. Add broccoli to the cheese sauce and pour into buttered casserole dish.

Melt remaining butter in a small skillet and stir in cracker crumbs. Cover the broccoli casserole with the buttered cracker crumbs. 

Bake until bubbly and lightly browned, about 20 minutes.