01 - Preheat the oven to 350°F. Grease a medium baking dish with butter or nonstick spray.
02 - Steam or blanch broccoli florets and carrot slices for 3-4 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, stirring constantly. Gradually whisk in milk and cook until mixture thickens and becomes smooth.
04 - Remove saucepan from heat. Stir in shredded cheddar cheese, garlic powder, onion powder, salt, and black pepper. Mix until cheese is fully melted and sauce is creamy.
05 - Gently fold broccoli and carrots into the cheese sauce until vegetables are evenly coated. Transfer mixture to the prepared baking dish.
06 - In a mixing bowl, combine panko breadcrumbs, melted butter, and Parmesan if using. Sprinkle topping evenly over the vegetable and cheese mixture.
07 - Bake for 25-30 minutes until the top is golden brown and bubbling. Allow casserole to rest for 5 minutes before serving.