Set the oven and prepare pan. Preheat the oven to 450°F and line a baking sheet with foil. Set aside.
Prepare brussels sprouts. Trim the ends from the brussles sprouts, and slice them in half if they're small, and in fourths if they're larger. Add them to a large mixing bowl and set aside.
Make the sauce and mix with sprouts. In a small sauté pan, melt the butter with the hazelnuts. Let it cook over low-medium heat just until it begins to brown, about 3 minutes after the butter melts. (Keep a close eye on this!) Mix in the lemon juice and pour it over the brussels sprouts and mix.
Roast. Add the sprouts to the foil-lined baking sheet and spread them out evenly. Use a rubber spatula to get all of the brown butter and nuts out of the bowl and onto the sprouts. Sprinkle lightly with salt and pepper.Place the baking sheet in the preheated 450°F oven and roast until the sprouts are golden brown and tender, about 20 minutes. They should be flipped/stirred mid-way through the cooking process. Cooking times may vary!