Mexican hot sauce,such as Cholula or Tapatio, for serving (optional)
In a medium mixing bowl beat eggs with a fork just until blended, set aside.
Heat a 10-inch non-stick skillet over medium-high heat. Crumble in chorizo and cook, while breaking up sausage and tossing, until browned and cooked through, about 5 - 6 minutes.
Transfer sausage to a sheet of foil lined with paper towels, wrap to keep warm. Leave rendered fat in skillet.
Pour 1 Tbsp oil into skillet with sausage drippings, heat over medium-high. Add potatoes (stand back the may splatter since frozen), season with salt and pepper to taste. Cook, tossing occasionally, until lightly browned and cooked through, about 7 - 8 minutes.
Transfer potatoes to a sheet of foil lined with paper towels, wrap to keep warm. There should be just a little oil left behind in the skillet if not drizzle in about 1/2 Tbsp olive oil.
Heat skillet over medium-low heat. Add eggs and cook, scrapping bottom of a pan constantly with a rubber spatula and folding edges of eggs inward, just until eggs are nearly set, season with salt and pepper. Remove from heat, cover and keep warm (they'll continue to cook from residual heat of pan).
Heat tortillas on a griddle, in a large skillet or in the microwave until heated through.
To assemble, layer 1/4 of the eggs in a row in the center of each tortilla. Top each with 1/4 of the potatoes. Divide cheese among each then sprinkle with sausage. Spoon a few big spoonfuls of pico de gallo over each, top with avocado.
Wrap two sides of tortilla inward then roll bottom side over, then roll up and wrap snuggly. Serve with Mexican hot sauce if desired.
*8 oz bacon (8 slices) can be substituted for chorizo.
Burritos can be made ahead and frozen, see notes above recipe for how-to.