Start by placing the masa harina in a large mixing bowl. Slowly add the warm water while stirring with your hands. Keep mixing until the dough comes together, and knead it for about 2 minutes until it’s smooth and soft. You should be able to form a ball without it cracking or sticking to your hands. If it’s too dry, add a tiny bit more water; if it’s too sticky, keep kneading it until the warmth of your hands brings it to the right consistency.
Shape the dough into a ball and cover the bowl with a towel. Let it rest for 10 minutes while you prepare the cheese, grating or slicing it if needed. After 10 minutes, knead the dough again for one minute. If it feels as though it has dried out slightly, wet your hands with warm water and knead it so that it is very soft and moist without being sticky.
Heat a griddle, comal or cast iron skillet on medium heat. Prepare your tortilla press by placing a small sheet of plastic covering both the bottom and top of the press. This will allow you to easily peel the tortillas away and place them on the griddle.
Form a ball of masa slightly smaller than a golf ball, about one inch in diameter and place it between the two sheets of plastic on the press. Then close the tortilla press and push the lever firmly- you want the tortilla to be as thin as possible. Open the press and slowly peel back the top piece of plastic from the tortilla. Place 1-2 tablespoons of grated or sliced cheese on one half of the tortilla. Keeping the plastic on the bottom of the tortilla, fold it in half. Press along the edges to seal the quesadilla. Peel back one side of the plastic then place the quesadilla, masa side down, on your left hand and peel back the plastic on the other side. Slowly lay the quesadilla onto the pan. Cook for about 2-3 minutes on the first side, or until the edges become dry and begin to lift from the pan. Flip the tortilla and cook for another 2 minutes on the other side. You want them to be lightly browned but not crispy. Check to make sure all areas of masa are cooked, the tortilla should look dry and not doughy.
Once your quesadilla Mexicana is golden brown and melty, remove it from the comal and serve it hot. Serve with your favorite salsa, guacamole, or sour cream!