Preheat your oven to 400°F (200°C). On a large baking sheet, toss the chopped carrots, parsnips, and onion with olive oil, salt, and pepper. Roast for 20 minutes, or until they begin to soften.

While the root vegetables are roasting, bring a large pot of salted water to a boil. Blanch the broccoli and cauliflower florets for 2-3 minutes. Immediately transfer them to an ice bath to stop the cooking process, then drain well.

In a large saucepan over medium heat, melt the butter. Whisk in the flour and cook for 1 minute until it forms a smooth paste.

Gradually whisk in the warm milk until the mixture is smooth. Bring to a simmer, stirring constantly, until the sauce thickens (about 5-7 minutes). Remove from heat and stir in the minced garlic, cheddar, Gruyère, and 1/4 cup of Parmesan cheese. Stir until the cheese is completely melted and smooth. Season with salt, pepper, and nutmeg.

In a large bowl, combine the roasted root vegetables and the blanched broccoli and cauliflower. Pour the cheese sauce over the vegetables and gently toss to coat everything evenly. Transfer the mixture to a greased 9x13 inch baking dish.

Sprinkle the remaining 1/4 cup of Parmesan cheese over the top. Bake for 20-25 minutes, or until the sauce is bubbly and the top is golden brown. Let it rest for 10 minutes before serving.