If needed, you can roast garlic ahead of time! A day or two is fine. After roasted, let the garlic cool then squeeze the cloves out, making sure to remove any of the paper. Use a fork and mash the garlic well until it is creamy and spreadable.
Preheat oven to 350 degrees F. Slice baguette into 1/2-inch rounds and place on a baking sheet. Drizzle with 2 tablespoons of olive oil. Bake for 8-12 minutes, rotating the pan halfway through.
While the bread is toasting, heat a large skillet oven medium heat. Add remaining olive oil, then toss in brussels sprouts, salt, pepper and nutmeg, tossing well to coat. Cook for 10 minutes, stirring occasionally, until warm, wilted, slightly crispy and even a little golden. Stir in grated parmesan cheese, mixing well to coat and turn off heat.
Spread a bit of mashed roasted garlic onto each piece of crostini. To serve, top crostini with a spoonful of sprouts, then add a shaving of fresh parmesan cheese and some cracked black pepper.