Preheat the oven to 400°F (200°C).

Toss the halved Brussels sprouts with olive oil, salt, and pepper.

Spread them out on a baking sheet and roast for 20-25 minutes, until they are tender and lightly browned.

In a medium saucepan, melt the butter over medium heat.

Whisk in the flour and cook for about 1 minute to form a roux.

Gradually add the milk, whisking continuously to avoid lumps.

Cook the sauce, whisking constantly, until it thickens and begins to bubble.

Reduce the heat to low and stir in the grated Gruyere cheese, Dijon mustard, salt, pepper, and nutmeg (if using).

Continue to stir until the cheese is fully melted and the sauce is smooth.

Transfer the roasted Brussels sprouts to a greased baking dish.

Pour the Dijon Mornay sauce over the Brussels sprouts and stir gently to combine.

Sprinkle the top with grated Parmesan cheese and bread crumbs.

Bake in the preheated oven for 15-20 minutes, until the top is golden brown and the sauce is bubbly.

Let the gratin cool slightly before serving.