Peel the chayotes and cut them into chunks. Remove the seed if it is large or fibrous.
Bring a large pot of lightly salted water to a boil. Add the chayote and cook for 10–12 minutes, or until fork-tender.
Drain well and let cool slightly.
Transfer the cooked chayote to a clean kitchen towel and gently squeeze out excess moisture.
Finely chop or lightly mash the chayote until you have about 2 cups.
In a large bowl, combine the chayote, egg yolks, queso fresco, salt, and pepper.
In a separate bowl, beat the egg whites until stiff peaks form.
Fold one-third of the egg whites into the chayote mixture to lighten it. Gently fold in the remaining egg whites until no streaks remain.
Heat about ¼ inch of oil in a large skillet over medium heat.
Scoop about ¼ cup of batter into the skillet for each tortita and gently flatten.
Fry for 2–3 minutes per side, or until golden brown and puffed.
Transfer to a paper towel-lined plate and repeat with the remaining batter.