Soften the tortillas by briefly toasting them directly over a burner on the stove (electric is fine) for a minute or two, flipping frequently. Spoon 1 tablespoon of mashed potato into the center of each tortilla. Flatten out the potato, leaving a 1-inch border. Lay 2 pieces of Manchego and 2 slices pickled jalapeño onto each tortilla, and fold into a half-moon shape.

In a large skillet over medium heat, melt half the butter. Gently set four of the tacos in the pan and cook until nicely browned, 3 to 4 minutes on each side. Drain on paper towels. Repeat with the remaining butter and tacos. Cut the tacos in half before serving with salsa.