Steam the broccoli and cauliflower florets for 3-4 minutes until they are bright and slightly tender.
Melt 6 tablespoons of butter in a large skillet over medium heat.
Add the diced onion and minced garlic to the skillet. Sauté until the onion becomes translucent, about 3-4 minutes.
Sprinkle the all-purpose flour over the onion and garlic mixture. Whisk to combine and cook for an additional 45 seconds.
Slowly pour in the chicken broth while whisking constantly. Cook until the sauce begins to thicken, then add the milk and continue to whisk.
Once the sauce has thickened, add the shredded cheddar cheese, stirring until it is fully melted and combined. Season with salt and pepper to taste.
Combine the steamed broccoli and cauliflower with the cheese sauce, then transfer the mixture to a baking dish.
Sprinkle breadcrumbs over the top of the casserole. Bake at 350°F for 25 minutes or until the top is golden brown and the sauce is bubbly.