Preheat oven to 425 degrees. On a rimmed baking sheet, drizzle peppers and carrots with olive oil and season with salt and pepper. Roast, flipping once, until golden brown and tender, about 20 minutes.
Arrange roasted carrots and peppers with the citrus on a platter. Top with crumbled goat cheese and hazelnuts. Whisk vinegar and remaining 2 tablespoons oil; season with salt and pepper. Drizzle over vegetables.