Preheat your oven to 350°F (175°C).

In a large pot, bring salted water to a rolling boil, add broccoli, cauliflower, and carrots. Blanch for 2-3 minutes, drain and set aside.

In a large skillet, heat olive oil over medium heat. Add onion and garlic, sauté for about 5 minutes until soft.

Add mushrooms to the skillet and cook for an additional 5 minutes, until browned.

Combine the blanched vegetables, sautéed onion and mushroom mixture, and frozen peas in a large mixing bowl.

In a separate bowl, mix shredded cheddar cheese, sour cream, and mushroom soup with salt, pepper, and thyme.

Pour the cheese sauce over the vegetable mixture and toss gently until fully coated.

Transfer the combined mixture to a greased 9x13-inch baking dish.

Mix bread crumbs and grated Parmesan, then sprinkle over the casserole.

Bake for 25-30 minutes until golden brown and bubbly.

Let it rest for about 5 minutes before serving.