Preheat the Oven: Preheat your oven to 400°F (200°C) and lightly grease a large baking dish or casserole dish.

Prepare the Vegetables: In a large bowl, toss the broccoli and cauliflower florets with 2 tablespoons of the garlic-flavored olive oil. Season with salt and pepper to taste. Spread the vegetables in an even layer on a large baking sheet and roast in the preheated oven for 15-20 minutes, or until they are tender and slightly golden.

Sauté the Onions and Garlic: While the vegetables are roasting, heat the remaining 1 tablespoon of garlic-flavored olive oil in a large skillet over medium heat. Add the sliced onions and cook, stirring frequently, until they are soft and caramelized, about 10 minutes. Incorporate the minced garlic and sauté for another 1-2 minutes until aromatic. Remove from heat and set aside.

Prepare the Cheese Sauce: In a medium saucepan, whisk together the cornstarch and evaporated milk until smooth. Place over medium heat and cook, stirring constantly, until the mixture begins to thicken, about 5-7 minutes. Remove from heat and stir in half of the cheddar cheese, Dijon mustard, and smoked paprika until the cheese is melted and the sauce is smooth.

Combine and Bake: In the prepared baking dish, combine the roasted broccoli and cauliflower with the caramelized onions. Pour the cheese sauce over the vegetables and gently mix to ensure everything is well coated. Sprinkle the remaining cheddar cheese and the mozzarella cheese evenly over the top.

Bake: Place the casserole in the oven and bake for 15-20 minutes, or until the cheese is bubbly and golden brown on top.

Serve: Remove the casserole from the oven and let it cool for a few minutes before serving. Enjoy this creamy, cheesy vegetable bake as a hearty side dish or a satisfying vegetarian main course!