01 - Preheat 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 and set aside.
03 - In a medium saucepan over medium heat, melt 2 tablespoons butter. Whisk in flour and cook for 1 minute, stirring constantly.
04 - Gradually whisk in milk until the mixture is smooth and thickened. Remove from heat and stir in shredded cheddar, garlic powder, onion powder, salt, and pepper; mix until cheese melts and sauce is creamy.
05 - Gently fold broccoli and carrots into the cheese sauce. Transfer mixture evenly to the prepared baking dish.
06 - In a mixing bowl, combine panko breadcrumbs, melted butter, and Parmesan cheese, if using. Sprinkle mixture evenly over the vegetables.
07 - Bake for 25 to 30 minutes, or until the topping is golden and the casserole is bubbling. Rest for 5 minutes before serving.