First, peel the potatoes, and slice them vertically into ¼ inch slices. Cut each of those slices into thin fries. Place all the fries in a large bowl of cold water.
Next make the Tomato Salsa: Simply mix all the ingredients together and set them aside.
Next, make the Cheddar Sauce: In a small bowl toss together the cheese and cornstarch. In a three- quart saucepan, bring the milk to a simmer. Turn the heat to low and whisk in the cheese. Whisk until the sauce thickens. Pour it into a bowl. You can reheat it in the microwave for a minute right before serving.
In a Dutch oven, heat one inch of oil to 325° using your deep fry thermometer. When the oil reaches that temperature, drain your fries from the water, and using towels, dry them off well.
Fry one quarter of the fries, just until they start to turn golden. Drain them on a wire rack, in a small pile. Repeat with the other 3 batches of potatoes.
Bring the oil up to 375° and refry the first batch of fries until golden brown. Repeat with the other 3 batches, draining each on the wire rack, and sprinkling each batch with salt right away.
Place the fries on a serving platter and top them with as much cheese sauce as you like and the Tomato Salsa.