Pork can be marinated up to 2 days.

For chile-marinated pork
6 dried guajillo chiles* (1 1/2 oz)
1 dried ancho chile* (1/2 oz)
4 thin (1/2-inch) rib pork chops (1 lb total), bones discarded
1/2 teaspoon cumin seeds
1/4 teaspoon black peppercorns
1 whole clove
1 (1/2- by 1/4-inch) piece cinnamon stick
2 tablespoons cider vinegar
2 large garlic cloves, quartered
1 teaspoon dried oregano (preferably Mexican), crumbled
1 teaspoon salt
2 to 3 tablespoons vegetable oil

For sandwiches
4 Mexican cemita rolls** or 8 sesame seed hamburger buns
2 ripe California avocados
1/2 cup fresh papalo leaves*** or cilantro leaves
6 oz Oaxacan string cheese*** or other string cheese, finely shredded with your fingers (1 1/2 cups)
4 canned chipotle chiles in adobo (optional), finely chopped
1/2 large white onion, thinly sliced
1 large plum tomato, thinly sliced crosswise

Prepare chiles and pork:
Discard chile stems and cut guajillo and ancho chiles open lengthwise with kitchen shears. Discard seeds and ribs.

Heat a dry 10- to 12-inch heavy skillet or griddle over moderate heat until hot, then toast chiles, a few at a time, turning and pressing down with tongs, until softened and fragrant, about 10 seconds per side.

Transfer chiles to a bowl, then cover with hot water and soak until softened, about 20 minutes.

Flatten pork while chiles soak:
Trim fat and sinews from pork and pound between 2 sheets of wax paper with flat side of a meat pounder or with a rolling pin until meat is about 1/8 inch thick.

Marinate pork:
Heat skillet over low heat until hot then toast cumin, peppercorns, clove, and cinnamon, stirring constantly, until fragrant and cumin is a shade darker, about 1 minute. Transfer hot spices to a blender and add vinegar, garlic, oregano, salt, and soaked chiles with about 1/3 cup soaking water, then blend until smooth. Transfer half of chile paste to an airtight container and chill or freeze for another use, then put remainder in a small bowl.

Spread a thin layer of chile paste in middle of a sheet of plastic wrap large enough to wrap all of meat and put 1 pork chop over paste. Spread a thin layer of chile paste on top, then continue layering meat, spreading each piece with chile paste. Wrap stacked pork in plastic wrap and marinate, chilled, at least 2 hours.

Cook pork and assemble sandwiches:
Heat 1 1/2 tablespoons oil in a 12-inch heavy skillet over moderately high heat until hot but not smoking. Season pork chops with salt and sauté, in batches, adding more oil as necessary, until just cooked through, 1 to 2 minutes per side. Transfer chops as cooked to a sheet of foil and keep warm wrapped in foil.

Preheat broiler. Cut rolls in half horizontally and arrange, cut sides up, on a large baking sheet. Broil buns about 6 inches from heat until golden, about 1 minute.

Halve, pit, and lightly mash avocados in peel with a fork, then spread thickly on cut sides of rolls. Season avocado with salt, then top with papalo. Make sandwiches with pork, cheese, chipotles (if using), onion, and tomato, pressing sandwiches together.