Begin by peeling potatoes and cutting them into uniform pieces.
Boil the potatoes until they are fork-tender, which should take about 15 minutes.
Once the potatoes are cooked, drain them and transfer them to a large bowl.
Use a potato masher to mash the potatoes until they are smooth.
Add salt, black pepper, garlic powder, cheddar cheese, and cornstarch to the bowl and mix with a wooden spoon until everything is well incorporated.
Spread a large sheet of waxed paper on a work surface and place the potato mixture on top.
Use an offset spatula to spread the mixture into a rectangle that is 8 x 10 inches and about ¾ to 1 inch thick.
Transfer the potato rectangle to the freezer for 30 minutes.
Once the potatoes have chilled, heat a Dutch oven with 1 inch of vegetable oil.
Using a pizza cutter or chef's knife, cut the potato rectangle into even French fries that are ¾ to 1 inch wide.
Once the oil has reached 325 degrees Fahrenheit, add 3-5 fries to the Dutch oven carefully. Cook the fries and rotate them with tongs if necessary until they are golden brown, which should take about 5-7 minutes per batch.
Transfer the cooked fries to a paper towel-lined plate and continue until all fries are cooked.
Enjoy the fries immediately with ketchup or aioli.
