Heat oil in a large skillet over medium-high heat; fry tortilla triangles until just starting to turn golden brown and crisp, 3 to 5 minutes. Add salsa; reduce heat to medium-low. Carefully mix tortillas and salsa with a spatula; cook 5 minutes.
Beat eggs, salt, and black pepper together in a small bowl; add to tortilla mixture. Increase heat to medium-high; gently scramble eggs until just set. Top with pepper Jack cheese, cover skillet, and turn off heat. Let sit for 3 minutes until cheese is melted.
