Preheat oven to 450 degrees. Heat a rimmed baking sheet in oven for 15 minutes. Meanwhile, toss brussels sprouts with 2 tablespoons oil, 1 teaspoon salt, and 1/4 teaspoon pepper. Spread onto heated baking sheet, and roast, stirring occasionally, until golden brown and crisp in spots, 12 to 15 minutes.
Heat a large nonstick skillet over medium-high heat. Add remaining tablespoon oil and the scallops. Season with salt, and sear for 4 minutes. Flip scallops, season with salt, and cook until opaque, about 3 minutes. Serve brussels sprouts and scallops drizzled with Hazelnut Vinaigrette. Garnish with hazelnuts.