Adjust the oven rack to the middle position and preheat to 450°F.
Make Cracker Topping:
Mix crushed crackers, 4 tablespoons of melted butter, ¼ shredded cheese, ¼ teaspoon salt, and ¼ pepper in a medium bowl.
Make the Sauce and Filling:
Melt the remaining 2 tablespoons of butter in a large pot or Dutch oven over medium heat. Add the garlic and flour and stir constantly for 1-2 minutes or until golden and fragrant.
Whisk in the heavy cream and chicken broth, breaking apart any clumps.
Add the thawed broccoli, cauliflower, dry mustard, ½ teaspoon salt, and ½ teaspoon pepper. Stir and bring the mixture to a boil.
Reduce the heat to medium-low and simmer covered for 5-8 minutes or until tender.
Remove the pot from the heat and stir in the remaining 1 ¾ cup shredded cheese.
Assemble Casserole:
Pour the mixture into a greased 9x13-inch baking dish.
Sprinkle the cracker topping over the casserole.
Bake, Cool, and Serve:
Bake in a preheated 450° oven for 10-15 minutes or until the topping is golden brown.
Cool the casserole for 10 minutes before serving.
Notes
Please shred your own cheese. The pre-shredded variety has starches and other agents added to it to prevent clumping. These additives aren’t the best when you’re making a cheese sauce!
Use a high-quality cheddar for the best results. I personally love Kerrygold and Tillamook.