Preheat your oven to 350°F (175°C).
In a saucepan, melt the butter over medium heat. Add the flour and whisk together until it forms a paste (roux).
Gradually add the milk to the roux, whisking constantly until the sauce thickens. This should take about 5 minutes.
Once thickened, add the cream cheese, garlic powder, onion powder, salt, and pepper. Stir until the mixture is smooth and the cheese has melted.
In a large mixing bowl, combine the broccoli, cauliflower, carrots, and bell pepper. Pour the cheese sauce over the vegetables and mix well to ensure the veggies are evenly coated.
Transfer the cheesy vegetable mixture into a greased 9x13 inch baking dish. Sprinkle the shredded cheddar cheese on top.
Bake in the preheated oven for 20 minutes, or until the cheese is bubbly and golden.
Remove from the oven and let it cool for a few minutes before serving.