Combine chorizo and onion in medium skillet and cook over medium-high heat until chorizo is cooked through and onions are soft, stirring often, about 10 minutes. Transfer mixture to paper-towel-lined plate to drain.
For each sandwich, layer bottom slice of bread, in this order, with 3 slices Pepper Jack, half chorizo-onion mixture, half the potato puffs, 3 American Cheese slices and pickled jalapeños, if using. Finish with remaining American Cheese slices and top with remaining bread slices.
Butter sandwich tops and bottoms with 1 tablespoon of butter per bread slice. Place sandwiches in preheated nonstick skillet and grill, covered, over low heat, flipping as needed, until cheese is melted and bread is brown and crispy. Serve with side of sour cream.