In a nonstick pan, heat the oil over medium-high heat. Add the hash browns, season with a pinch of salt and cook until golden brown, stirring occasionally, about 10 minutes. Remove from the pan and place on a plate lined with a paper towel. Carefully wipe out the pan.
Lower the heat to medium and cook the chorizo until crispy, breaking it up with a wooden spoon as it cooks, about 7 minutes. Transfer the cooked chorizo to the plate with the hash browns. Carefully wipe out the pan.
Whisk the eggs together and season with a pinch of salt and pepper.
Return the pan to medium heat and melt the butter; then pour in the eggs.
Lightly scramble the eggs and then let settle in a thin layer covering the bottom of the pan.
Sprinkle with the cheddar cheese. When it begins to melt, place a tortilla on top, allowing it to stick to the cheese. Flip the whole thing over.
Sprinkle the Oaxaca cheese evenly over the egg. On one half of the quesadilla, add the chorizo, hash browns, salsa, avocado, cilantro and scallions.
Fold the side without the filling over, creating a half circle, and press down with a spatula.
Transfer to a cutting board and slice into 4 equal pieces. Serve hot with lime wedges and sour cream and salsa for dipping.