Heat the oil in a large nonstick skillet over medium-high heat. Add the chorizo and cook, breaking it up into small pieces, until cooked through and crisp, about 5 minutes. Transfer to a paper-towel-lined plate using a slotted spoon. Add the hash browns to the skillet and cook, stirring occasionally, until the potatoes are golden brown and crisp, 8 to 10 minutes. Beat together the eggs, a pinch of salt, a few grinds of pepper and a few dashes of hot sauce in a medium bowl until well blended. Return the chorizo to the pan and pour the eggs over the potatoes and chorizo and cook, stirring, until the eggs are fluffy and just set, about 3 minutes. Remove from the heat and stir in the cilantro.
Working with one tortilla at a time, warm in a large nonstick skillet set over medium heat until pliable. Top with one-quarter of the avocado and egg mixture, 1 tablespoon of the pico de gallo and 2 tablespoons of the cheese. Fold in the two sides and roll up tightly from the bottom to the top. Repeat with remaining tortillas and burrito fillings. Serve with the remaining pico de gallo on the side.
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