Preheat oven to 450 degrees F.
In a medium bowl, add the crushed Saltine crackers, 4 tablespoons of melted butter, 1/4 cup of shredded cheddar cheese, 1/4 teaspoon salt, and 1/4 teaspoon pepper. Stir to combine and then set aside.
In a large pot over medium heat, add the remaining 2 tablespoons of butter, garlic, and flour. Stir constantly until golden and fragrant, about 1-2 minutes.
Slowly whisk in the cream and broth.
Stir in broccoli, cauliflower, dry mustard, 1/2 teaspoon salt, and 1/2 teaspoon pepper. Bring to a boil and then reduce heat to medium-low and simmer covered, stirring occasionally, until broccoli and cauliflower are nearly tender, about 5-8 minutes.
Remove pot from heat and stir in remaining cheese until incorporated. Pour mixture into a 9x13-inch dish.
Top with cracker crumbs.
Bake for 10-15 minutes, or until crumbs are golden brown and crisp. Cool for 10 minutes before serving.