Preheat your oven to 400˚F (200˚C). Drizzle a little olive oil on the bottom of a square baking dish and spread it around. Set aside.

In a large skillet, bring ½ inch of salted water to a boil. Add the broccoli and cauliflower; cover and cook over high heat until crisp-tender, about 4 minutes. Drain the vegetables in a colander and set aside.

Wipe out the skillet, add 2 tablespoons of olive oil, and heat over medium-high heat. Add the sliced onions and cook for 2 to 3 minutes, or until softened.

Stir in the minced garlic and continue to stir and cook for 1 minute. Add the broccoli and cauliflower to the skillet. Season with salt and pepper and continue to cook for about 2 minutes, or until lightly golden. Remove from heat and transfer the vegetables to the baking dish; set aside.

Wipe the skillet and add 1 tablespoon of olive oil, ¾ cup of shredded cheddar cheese, cornstarch, evaporated milk, mustard, salt, pepper, and paprika.

Cook over low heat, stirring constantly with a whisk until the mixture is melted and thickened, about 2 minutes.

Pour the cheese sauce over the broccoli and cauliflower and stir to combine. Sprinkle the remaining cheeses over the top.

Bake for 20 minutes or until lightly browned and bubbly. Remove from the oven and let stand for 5 to 8 minutes before serving.