Use a vegetable peeler and remove the skin of each carrot (optional - if you like the skin you can leave it on). Use a knife and chop off the head/root of each carrot.
Cut each carrot in half, lengthwise and then in half again.
Line a baking sheet with parchment paper, then add the carrots to the baking sheet. Drizzle olive oil over the carrots. Sprinkle salt, cheese, pepper, and fresh thyme.
Bake for 35 minutes. While the fries are baking, make the aioli by combining all of the ingredients in the small bowl.
Once the fries are finished, remove the baking sheet from the oven and add the remaining shredded parmesan. Serve hot with Parmesan Aioli.