01 - Preheat oven to 350°F (180°C). Grease a medium baking dish with butter or nonstick spray.
02 - Steam or blanch broccoli florets and carrot slices in simmering water for 3 to 4 minutes until just tender. Drain thoroughly and set aside.
03 - In a medium saucepan over medium heat, melt 2 tablespoons butter. Whisk in flour and cook for 1 minute until smooth and bubbling. Gradually add milk, whisking constantly, until sauce thickens.
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 drained broccoli and carrots into the cheese sauce until vegetables are evenly coated. Transfer mixture to the prepared baking dish.
06 - In a small bowl, combine panko breadcrumbs, melted butter, and grated Parmesan. Sprinkle evenly over the vegetable mixture in the baking dish.
07 - Bake for 25 to 30 minutes until the topping is golden brown and the casserole is bubbling. Allow to rest 5 minutes before serving.