01 - Preheat the oven to 350°F. Lightly grease a medium-sized baking dish.
02 - Steam or blanch broccoli florets and carrot slices for 3 to 4 minutes until just tender. Drain thoroughly and set aside.
03 - In a medium saucepan over medium heat, melt 2 tablespoons butter. Whisk in the flour and cook for 1 minute to form a roux.
04 - Gradually whisk in the milk and continue cooking until the mixture thickens. Remove from heat and stir in shredded cheddar cheese, garlic powder, onion powder, salt, and black pepper until cheese is fully melted and sauce is smooth.
05 - Fold the prepared broccoli and carrots into the cheese sauce. Transfer the mixture evenly into the greased baking dish.
06 - In a mixing bowl, combine panko breadcrumbs, melted butter, and optional Parmesan cheese. Distribute the topping evenly across the vegetable mixture.
07 - Bake for 25 to 30 minutes, or until the topping is golden and the filling is bubbling. Allow the casserole to rest for 5 minutes before serving.