Wash and scrub the potatoes, then slice into fry shapes. Place in a bowl and fill the bowl with water to cover the potatoes. Let soak for 20-30 minutes.
Preheat the oven to 425 degrees Fahrenheit. Drain the water from the bowl, place the potatoes on paper towels, and dry thoroughly. Wipe down the bowl to dry then return the potatoes to the bowl. Drizzle with the avocado oil and sprinkle with the cornstarch. Toss to coat the potatoes with the oil and cornstarch, then spread evenly on 1-2 large baking sheets.
Bake in the preheated oven for 15-20 minutes, flipping halfway through, until fork tender and browned. Broil on high for 2-4 minutes if desired for further browning.
While the potatoes are roasting, make the queso fresco aioli: Add all ingredients for the aioli to a food processor and pulse until smooth, scraping down the sides as necessary.
Serve the roasted potato fries with the queso fresco aioli to dip!