Preheat oven to 375°F (190°C). Lightly grease a 9x13 inch baking dish.

Bring a large pot of salted water to a boil. Add broccoli florets, cauliflower florets, and diced carrots. Cook for 3-4 minutes, until tender-crisp. Drain well and immediately plunge into an ice bath to stop cooking if desired, then drain again thoroughly. (This step ensures vegetables retain color and a slight bite.)

In a large bowl, combine the blanched vegetables with diced zucchini and frozen peas. Set aside.

In a large skillet or Dutch oven, melt 3 tablespoons of butter over medium heat. Add the flour and whisk constantly for 1-2 minutes to create a roux.

Gradually whisk in the milk and vegetable broth until smooth. Continue whisking and cook for 3-5 minutes, until the sauce thickens.

Stir in Dijon mustard, garlic powder, onion powder, black pepper, and salt.

Remove from heat. Add 3/4 cup of the shredded sharp cheddar cheese and all of the Gruyere cheese (if using). Stir until the cheese is melted and the sauce is smooth. Taste and adjust seasoning if needed.

Pour the prepared cheese sauce over the mixed vegetables in the large bowl. Gently toss until all vegetables are evenly coated.

Transfer the vegetable mixture to the greased 9x13 inch baking dish, spreading it into an even layer.

In a small bowl, combine the panko breadcrumbs, grated Parmesan cheese, and melted butter. Sprinkle this topping evenly over the vegetables in the baking dish. Then, sprinkle the remaining 1/4 cup of sharp cheddar cheese over the breadcrumb topping.

Bake for 25-30 minutes, or until the casserole is bubbling around the edges and the topping is golden brown and crispy.

Let the casserole stand for 5-10 minutes before serving to allow it to set slightly.