01 - Preheat oven to 350°F (180°C). Lightly grease a medium baking dish.
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 butter. Whisk in flour and cook for 1 minute until slightly foamy. Gradually whisk in milk until smooth and thickened, about 2 to 3 minutes.
04 - Remove saucepan from heat and incorporate shredded cheddar, garlic powder, onion powder, salt, and black pepper. Stir until the cheese is melted and sauce is creamy.
05 - Gently fold blanched broccoli and carrots into cheese sauce. Transfer mixture into prepared baking dish and spread evenly.
06 - In a separate bowl, combine panko breadcrumbs, melted butter, and grated Parmesan if using. Sprinkle this mixture evenly over the vegetable-cheese mixture.
07 - Bake for 25 to 30 minutes until topping is golden and filling is bubbling. Allow to rest for 5 minutes before serving.