Heat olive oil in a large skillet over medium heat. Add diced potatoes, season with salt and pepper, and cook until golden and tender.
In a bowl, whisk the eggs lightly with a pinch of salt and pepper.
Reduce heat to medium-low and pour eggs into the skillet with the potatoes. Stir gently to scramble until eggs are mostly set but still soft.
Add roasted green chiles and stir gently to combine.
Sprinkle shredded cheese over the egg mixture and let it melt naturally. Remove from heat.
Warm tortillas in a skillet or microwave until flexible.
Spoon the egg mixture into the center of each tortilla, fold the sides inward, and roll tightly into burritos.
Serve warm or wrap for later use.
