First cook the potatoes. Heat your non-stick skillet to medium-high and add 1 tablespoon neutral oil. Once it's hot, add the cubed potatoes, sprinkle with 1 teaspoon salt and ½ teaspoon pepper, and cook stirring occasionally for 25-30 minutes until tender. Set aside.
Then make the eggs. In a large bowl, whisk together the eggs with ½ teaspoon salt and ¼ teaspoon pepper. In the same non-stick skillet that you cooked the potatoes in, cook the eggs on medium-low heat stirring the entire time (helps make them fluffy), until cooked through to your liking. About 5-10 minutes.
Prep the pico de gallo. In a small bowl, combine the chopped tomato, onion, jalapeño, lime juice, salt, and pepper.
To assemble, take one of your tortillas, and slightly off centered (closer to you) in a log shape, lay down the toppings in the following order using ¼ of the toppings for each burrito: beans - potatoes - pico de gallo - avocado - eggs - cheese.
To wrap the burritos, first fold in the sides of the tortilla over the filling, then take the side closest to you and fold over the filling, tucking the filling in. Then roll over itself away from you as tightly as you can without ripping the tortilla. Place fold-side down. Repeat 3 more times.
Into the same non-stick skillet you used before heated to medium, place the burritos fold-side down. Cook on the first side for about 3-5 minutes until golden brown, then flip and cook on the other side for another 3-5 minutes until golden brown. The cheese will help seal them shut.
Serve with hot sauce/sour cream/salsa.