Peel the green plantain and slice into 1/2-inch thick rounds.
Heat the avocado oil in a large non-stick skillet over medium-high heat.
Place the plantain slices in the skillet and cook for 3-4 minutes per side until golden and softened.
Remove plantains from the pan, lightly smash them with the back of a wooden spoon or a flat plate, and return to the pan for 1-2 more minutes per side to get extra crispy.
Slice the queso de freir into rectangles and add to the skillet, searing for about 2 minutes per side until a deep brown crust forms.
In a small bowl, whisk together the large eggs, egg whites, sea salt, and black pepper.
Push the plantains and cheese to one side of the pan and pour the egg mixture into the empty space.
Gently scramble the eggs with a spatula until they are just set and fluffy.
Plate the crispy plantains, fried cheese, and eggs together, then garnish with fresh chopped cilantro.