01 - Preheat oven to 350°F. Grease a medium-sized baking dish with butter or nonstick spray.
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 of butter. Whisk in the flour and cook for 1 minute, stirring continually. Slowly add milk, whisking until mixture is smooth and begins to thicken.
04 - Remove saucepan from heat. Stir in shredded cheddar cheese, garlic powder, onion powder, salt, and black pepper. Mix until cheese is completely melted and sauce is smooth.
05 - Gently fold steamed broccoli and carrots into the cheese sauce, coating evenly. Transfer mixture into the prepared baking dish.
06 - In a small mixing bowl, combine panko breadcrumbs, melted butter, and optional grated Parmesan. Evenly sprinkle breadcrumb mixture over the casserole.
07 - Bake in the preheated oven for 25 to 30 minutes, or until the topping is golden brown and the edges are bubbling. Allow to rest 5 minutes before serving.