Heat the oil in a large nonstick skillet over medium-high heat. Add the hash browns and cook, stirring occasionally, until golden brown and crisp, 8 to 10 minutes.
Meanwhile, beat the eggs in a medium bowl with the chipotle powder, a sprinkle of salt and a few grinds of pepper until well blended. Pour the eggs over the cooked potatoes and cook, stirring, until the eggs are fluffy and just set, about 3 minutes. Remove from the heat and stir in the cilantro.
Warm a tortilla in a large nonstick skillet over medium heat it is until pliable. Top with one-quarter of the avocado slices, one-quarter of the egg mixture and 2 tablespoons each of the Monterey jack and Cheddar. Fold in the two sides and roll up tightly from the bottom to the top. Repeat with remaining tortillas and burrito filling. Serve with salsa on the side.
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