Heat a large non-stick skillet over medium heat. Add the chorizo, breaking it into small pieces with a spatula, and cook for eight to ten minutes until fully cooked. Drain excess fat, leaving about 1 tablespoon in the pan. Transfer the cooked chorizo to a bowl.

Using the same skillet, melt one tablespoon of butter, combining it with the reserved chorizo fat. Pour in the whisked eggs, season with 1/2 teaspoon of salt and 1/4 teaspoon of black pepper, and cook, stirring frequently, until the eggs are soft but set, about ten minutes. Mix in the shredded cheddar and Monterey jack cheeses until melted. Transfer the scrambled eggs to a separate bowl.

In the same skillet, melt the remaining tablespoon of butter over medium-high heat. Add the shredded potatoes, spreading them evenly. Sprinkle with the remaining 1/2 teaspoon of salt and 1/4 teaspoon of pepper. Cook, stirring occasionally, until the potatoes become golden and crispy, approximately 10 minutes. Remove from heat.

To assemble the burritos, warm the tortillas in the microwave for about 30 seconds to make them more pliable. Distribute the potatoes, scrambled eggs, and chorizo evenly among the four tortillas. If using, sprinkle chopped parsley or cilantro over the chorizo.

To roll the burritos, fold one edge of the tortilla over the filling, tuck in the sides, and continue rolling tightly. Repeat with the remaining tortillas and filling.

Wrap each burrito in tin foil and place them on a baking sheet. Warm them in a preheated oven for five to ten minutes before serving.