01 - Preheat oven to 350°F. Lightly grease a medium 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 butter. Whisk in flour and cook for 1 minute, stirring constantly.
04 - Gradually whisk in milk until mixture is smooth and begins to thicken. Remove saucepan from heat and stir in cheddar cheese, garlic powder, onion powder, salt, and pepper. Continue mixing until cheese is completely melted and sauce is creamy.
05 - Fold the steamed broccoli and carrots into the cheese sauce, coating all pieces evenly. Transfer the mixture to the prepared baking dish.
06 - In a small mixing bowl, combine panko breadcrumbs, melted butter, and grated Parmesan if using. Sprinkle mixture evenly over the vegetables.
07 - Bake for 25 to 30 minutes, or until the topping is golden brown and the casserole is bubbling. Allow to rest for 5 minutes before serving.