Set a large cast iron skillet over medium-high heat. Once hot, drizzle in 2 tablespoons oil and add in the onions. Cook until they're soft and just beginning to brown, about 3 to 4 minutes. Add in the potatoes and cook, stirring often, until the potatoes have softened as well, another 5 minutes.
Move the potatoes and onions to one side of the skillet and then add the chorizo, breaking it up with a wooden spoon. Cook until just beginning to brown, before stirring in the potatoes and onions. Continue cooking, stirring often, for about 6 to 8 minutes. Remove from the heat and let cool.
Warm the tortillas on a dry skillet, over moderate heat, or directly on the stove burners (if you have a gas stove), just enough to make them pliable.
Working with one tortilla at a time, sprinkle half with a bit of cheese. Top with a few spoonfuls of the chorizo and potato mixture. Sprinkle with a bit more cheese and then fold over. Place on a baking sheet or platter and continue filling the rest.
Wipe out the skillet with a paper towel and drizzle with the remaining oil, set over medium-high heat. Once hot, place in two quesadillas and cook until crispy, about 1 to 2 minutes. Flip over and cook until the cheese has melted. Remove from the skillet and place on a wire rack, while you continue to cook the rest.
Arrange on a platter and top with pickled jalapeƱos and cilantro. Serve with sour cream and salsa on the side. Enjoy!