01 - Preheat oven to 350°F. Grease a medium baking dish with butter or nonstick spray.
02 - Steam or blanch broccoli florets and carrot slices in boiling water for 3 to 4 minutes until just tender. Drain well and set aside.
03 - In a medium saucepan over medium heat, melt 2 tablespoons butter. Whisk in flour and cook, stirring constantly, for 1 minute. Gradually pour in milk, whisking to form a smooth mixture. Cook until thickened, about 2 to 3 minutes.
04 - Remove pan from heat, add shredded cheddar cheese, garlic powder, onion powder, salt, and black pepper. Stir until cheese is melted and sauce is creamy and smooth.
05 - Gently fold steamed broccoli and carrots into the cheese sauce until evenly coated. Pour the mixture into the prepared baking dish.
06 - In a small bowl, mix panko breadcrumbs with melted butter and grated Parmesan cheese if using. Sprinkle evenly over the vegetable mixture.
07 - Bake uncovered for 25 to 30 minutes, or until the topping is golden brown and the edges are bubbling. Let rest for 5 minutes before serving.