Preheat your marquesita iron or traditional waffle maker to the highest setting. Beat together the eggs and egg whites with a handheld mixer for about 5 minutes, or until they become foamy and white in color.
Add the sugar, milk, vegetable oil, and vanilla extract to the egg mixture and beat on low speed until just incorporated. Sift the flour and salt together in a bowl, then add it to the egg mixture gradually while beating on low speed.
Spray your marquesita iron or waffle maker with non-stick cooking spray, then pour about 1/4 cup of batter onto each cooking compartment. Close the lid and cook for about 5 minutes.
Transfer the cooked marquesitas to a plate and let them cool. Once cooled, cut each one in half lengthwise so that you have four semicircles. Place the Edam cheese on top of each marquesita and close it with a toothpick.
Place them in the oven preheated to 350 F and bake for about 5 minutes, or until the cheese melts. Serve your marquesitas hot with a side of honey or syrup if desired. Enjoy!