For the best method to prepare the hazelnuts, see How to Peel Hazelnuts.

Combine the carrots, nuts, garlic, and cheese into a food processor and pulse until coarsely chopped.

With the motor running on low, drizzle in the oil until mixture comes together and is very finely chopped (do not over-process into a paste, you still want each ingredient identifiable). Season to taste with salt and pepper.

Toss cooked pasta with pesto, adding a bit more olive oil if you like to loosen the pesto (or you can save some pasta water and use that to thin the pesto).