01 - Preheat the oven to 350°F (180°C). Lightly grease a medium baking dish with butter or nonstick spray.
02 - Steam or blanch broccoli florets and sliced carrots for 3 to 4 minutes until just tender. Drain well and set aside.
03 - Melt 2 tablespoons butter in a medium saucepan over medium heat. Add flour and whisk constantly for 1 minute until smooth. Gradually whisk in the milk and cook, stirring, until the mixture thickens, about 3 minutes.
04 - Remove saucepan from heat. Stir in shredded cheddar cheese, garlic powder, onion powder, salt, and pepper. Mix until cheese is fully melted and sauce is creamy.
05 - Gently fold steamed broccoli and carrots into the cheese sauce. Transfer the mixture to the prepared baking dish, spreading evenly.
06 - In a small mixing bowl, combine panko breadcrumbs, melted butter, and grated Parmesan cheese if using. Sprinkle this mixture evenly over the vegetables in the baking dish.
07 - Bake uncovered in the preheated oven for 25 to 30 minutes, until the topping is golden and the casserole is bubbling. Let rest for 5 minutes before serving.