In a skillet or frying pan, heat 2 tablespoons of the olive oil and the garlic and onion over medium-low heat until the garlic and onion are slightly browned. Add the potatoes and the remaining olive oil and cook over medium heat—flipping and stirring occasionally.
While the potatoes cook, season them with the cayenne, oregano, salt and black pepper. Cover and cook for 25 to 30 minutes, or until the potatoes are tender in the middle (check with fork prongs). Reduce the heat to low.
Meanwhile, whisk the eggs in a bowl and add a pinch of salt and pepper, to taste. After the potatoes are cooked, pour in the egg mixture—stirring until the eggs are light and fluffy. When the eggs are almost finished cooking, sprinkle in the shredded cheese. Remove from the heat and keep warm.
Heat the flour tortillas on a low, open flame or stove burner for 5 to 10 seconds on each side. Fill the warmed tortillas with an equal mixture of eggs and potato—adding more cheese if desired. Top with avocado slices and, of course, plenty of salsa. Serve warm.