Heat oil in a large skillet over medium-high heat and pan-fry tortilla triangles until they are just starting to turn golden brown and crisp, 3 to 5 minutes. Add salsa, reduce heat to medium-low, and carefully mix tortillas and salsa with a spatula. Cook for 5 minutes.
Beat eggs, salt, and pepper in a small bowl. Add eggs to tortillas and increase heat to medium-high. Scramble eggs gently until just set. Top with pepper Jack cheese, cover, and turn off the heat. Let sit for 3 minutes until cheese is melted.