Preheat oven to 400°F. Trim carrot tops, leaving some stem attached. Measure out 2 cups carrot tops and set aside.
Toss carrots and vegetable oil on a rimmed baking sheet; season with salt and pepper. Roast, tossing occasionally, until carrots are golden brown and tender, 25-35 minutes. Let cool.
Pulse garlic and nuts in a food processor until a coarse paste forms. Add basil, Parmesan, and reserved carrot tops; process until a coarse purée forms. Add olive oil and pulse until combined; season with salt and pepper. Serve carrots with pesto.