01 - Preheat your oven to 400°F (200°C). Lightly grease a medium-sized baking dish.
02 - Bring a large pot of salted water to a rolling boil. Add the prepared Brussels sprouts and cook for 4 to 5 minutes, until they are just tender. Drain thoroughly and set aside.
03 - In a large skillet set over medium heat, melt 2 tablespoons of butter. Add the finely chopped yellow onion and sauté for approximately 3 minutes, until it becomes translucent. Stir in the minced garlic and cook for an additional minute.
04 - Pour the heavy cream and whole milk into the skillet. Stir in the Dijon mustard and ground nutmeg. Bring the mixture to a gentle simmer, then season generously with salt and freshly ground black pepper to your preference.
05 - Add the grated Gruyère cheese and half of the grated Parmesan cheese to the sauce. Stir continuously until the cheeses are fully melted and the sauce is smooth and well-combined.
06 - Gently add the blanched Brussels sprouts to the cheese sauce, tossing carefully to ensure each piece is coated. Transfer this mixture into the prepared baking dish, spreading it evenly.
07 - In a small mixing bowl, combine the fresh breadcrumbs with the melted butter and the remaining grated Parmesan cheese. Mix thoroughly until the breadcrumbs are evenly moistened.
08 - Evenly sprinkle the breadcrumb mixture over the Brussels sprouts in the baking dish. Place the dish in the preheated oven and bake for 20 to 25 minutes, or until the topping is golden brown and the sauce is bubbling.
09 - Allow the gratin to rest for 5 minutes before serving. If desired, garnish with fresh chopped parsley just before presenting.