Fill a large Dutch oven or casserole a little less than halfway with oil. Place over medium heat and bring to 325°F degrees — or test by dropping in a small piece of potato, if the oil bubbles all around it, it’s ready.
While the oil is heating up, fill a large bowl with ice water. Place a cooling rack on a baking sheet lined with paper towels. Cut the potatoes into 1/4-inch to 1/3-inch matchsticks. Add them to the ice water immediately after cutting, stirring occasionally to make sure the potatoes are not sticking to each other.
Remove about a quarter of the potatoes from the water. Pat dry with clean kitchen towels or paper towels. Once dry, carefully add them to the hot oil and fry for 2 to 3 minutes, stirring with tongs or a spider to make sure they aren’t sticking to each other. The fries should start to look creamy and matte in color. If they begin to brown, take them out. Transfer the fries to the baking sheet with the cooling rack and repeat the process with the remaining potatoes.
When all the potatoes have been fried and transferred to the baking sheet with the rack, raise the heat of the oil to 375°F to 400°F, or raise the heat under the casserole to medium-high.
While the oil is heating, crush the chiltepín chiles and mix with the salt, lime zest, a few cracks of black pepper, and the Cotija cheese. Set aside.
Once the oil is ready, add the fries back into the oil in 4 batches. Cook each batch for 3 to 4 minutes, or until the fries are golden brown. Transfer the fries back to the baking sheet with the rack.
If you are not going to eat immediately, keep warm in a 250°F oven. Just before serving, toss the finished fries in the cheese mixture until coated. Serve with habanero tartar sauce and/or ketchup.