In a Dutch oven or large heavy-bottomed pot, heat the oil to 350 degrees.
Add Doritos to a food processor and pulse until you have fine crumbs. Transfer to a bowl and set aside. Add eggs and flour into two separate bowls. Mix salt and pepper into flour. Dredge cheese sticks in flour shaking off the excess. Dip into egg mixture, and repeat. After the second coat in eggs, coat in Doritos. Place on a baking sheet.
Fry the cheese sticks in batches until golden brown, about 2 to 3 minutes. Remove to a cooling rack. Serve with queso or salsa.