Preheat oven to 350 degrees 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.
Recipe Courtesy of Food Network Kitchens