Heat the butter in a 10-inch skillet over medium heat. Add the eggs and cook and stir until they're just set. Remove the eggs from the skillet and keep them warm.
Heat the oil in the skillet over medium-high heat. Add the potatoes and cook for 10 minutes or until they're browned, stirring often. Add the picante sauce and heat to a boil. Reduce the heat to low and cook for 5 minutes.
Divide the potato mixture and eggs evenly among the tortillas. Top with the cheese and wrap the tortillas around the potato, egg and cheese filling.