01 - Preheat oven to 350°F. Lightly grease a medium-sized baking dish with butter or nonstick spray.
02 - Steam or blanch broccoli florets and carrot slices for 3–4 minutes until just crisp-tender. Drain thoroughly and set aside.
03 - In a medium saucepan over medium heat, melt 2 tablespoons butter. Whisk in flour and cook, stirring constantly, for 1 minute to form a roux.
04 - Gradually whisk in milk until mixture is smooth and thickened, about 2–3 minutes. Remove pan from heat and stir in shredded cheddar cheese, garlic powder, onion powder, salt, and black pepper until cheese is melted and sauce is creamy.
05 - Gently fold the drained broccoli and carrots into the cheese sauce until evenly coated. Transfer the mixture to the prepared baking dish and spread evenly.
06 - In a mixing bowl, combine panko breadcrumbs, melted butter, and grated Parmesan cheese if using. Toss to coat evenly, then sprinkle mixture across the top of the casserole.
07 - Bake for 25–30 minutes until the topping is golden brown and the filling is bubbling. Let rest for 5 minutes before serving.