Heat a non-stick pan over medium heat. Place a tortilla in the pan. Sprinkle about 2 tablespoons of cheese on half of the tortilla. Place 4 to 5 slices of tomatoes on the cheese. Pour a quarter of the beaten eggs onto the tomatoes. Then place 2 slices of ham onto eggs followed by a sprinkling of another 2 tablespoons of shredded cheese.
Using a spatula, fold tortilla in half over the filling. Allow eggs to cook and tortilla to brown for about 3 to 4 minutes. Flip quesadilla over and continue to cook for another 2 to 3 minutes. Repeat with the other 3 tortillas.
Cut each quesadilla into triangles and serve immediately.