Place the masa harina and salt in a large bowl and gradually pour in the water while mixing it with your hand. Knead for 5 minutes or until there are no dry spots in the masa and it is soft like playdough, pliable but not sticky. To test if the masa is too dry, roll a small piece of masa into a ball and lightly press it, if the edges crack, the dough is too dry. Add an additional 1/4 cup of water and knead again.
Divide the masa into 20 balls a little smaller than a golf ball (1.12 oz)(32g).
Lay a plastic liner ( I like to cut squares out of grocery bags) on the bottom surface of a tortilla press. Place a ball of masa in the center of the liner and lay a second liner on top of the ball. Use your fingers to lightly press down on the masa ball and close the press, push down the lever to apply pressure. The tortilla should be about 1/16 of an inch thick.
Open the tortilla press and set aside that tortilla, leaving it in the liners. Take two more liners, and repeat step 3, open the tortilla press, and place about 2 tablespoons of grated cheese in four quadrants (see photo above). Peel off the liner of the reserved tortilla and gently place over the cheese.
Using a knife or pastry cutter divide the tortillas into four equal parts. Using your fingers, seal the edges, and transfer to a sheet tray lined with parchment paper. Repeat with the rest of the masa.
Heat about 3 inches of oil in a large skillet, over medium-low heat, to about 350°F. To test the oil, drop a corner of the stuffed masa in the oil, if it sizzles it means it’s ready. Once the oil is hot drop in the chilaquiles in batches and fry them until golden brown, about 1 minute on each side. Transfer to a sheet pan lined with paper towels.