Preheat Oven: Preheat your oven to 360°F (180°C).

Prepare Cheeses: In a large bowl, combine all the grated cheeses and set aside.

Cook Broccoli: In a large pot of salted water, cook the broccoli florets for 3-4 minutes until tender but not mushy. Drain and set aside.

Cook Macaroni: Cook the macaroni to al dente, about 1-2 minutes less than the package instructions. Drain and set aside.

Make Cheese Sauce: While the pasta is cooking, melt the butter over low-medium heat in a large pot. Add the chopped onion and sauté until soft, about 5 minutes. Add the crushed garlic and cook for an additional minute. Add the flour and whisk over medium-low heat, cooking for a couple of minutes until golden.

Add Milk to Sauce: Gradually add the milk, whisking constantly until smooth. Cook for 5-6 minutes until the sauce thickens slightly.

Season Sauce: Remove the sauce from heat and season with salt, pepper, and nutmeg.

Add Cheeses to Sauce: Gradually add 3/4 of the cheese mixture to the sauce, whisking until melted after each addition.

Combine Pasta and Broccoli with Sauce: Drain the pasta and add it to the sauce along with the broccoli florets. Mix well to ensure everything is evenly coated with the cheese sauce.

Transfer to Baking Dish: Transfer the mixture to a 12-inch (30cm) round baking dish. Sprinkle the remaining 1/4 of the cheese on top.

Bake: Bake for 20-25 minutes, or until the top is golden brown and bubbly.