Heat lard in a large heavy pot over medium-high. Cook onion, stirring occasionally, until golden brown and softened, 6–8 minutes. Add ancho, guajillo, morita, and pasilla chiles and broth and bring to a boil. Cover pot, remove from heat, and let sit, stirring occasionally, 30 minutes to allow chiles to soften.
Meanwhile, toast coriander seeds in a dry small skillet over medium heat, swirling often and adding cumin seeds during the last 30 seconds, until fragrant, about 2 minutes. Let cool; finely grind in spice mill or with mortar and pestle.
Preheat oven to 250°. Transfer chile mixture to a blender; reserve pot. Add ground toasted spices, garlic, and oregano and purée until smooth, adding more broth if mixture is too thick or won’t blend, about 2 minutes. Reserve ¼ cup purée for masa and set aside until ready to use. Place pork shoulder, pork belly, bay leaf, salt, and remaining chile purée (about 1¾ cups) in reserved pot. Bring mixture to a boil, cover pot, and transfer to oven. Braise pork until very tender and it shreds easily, 2–2½ hours. Let cool 15 minutes, then skim fat from sauce; discard bay leaf.
Using a potato masher or a large fork, smash pork into sauce until meat is shredded and incorporated into sauce. Stir in vinegar; let cool.
Transfer filling to an airtight container and chill until pork is cold and firm, at least 3 hours.
Do Ahead: Filling can be made 3 days ahead. Keep chilled.
For Fresh Masa
Mix masa, lard, broth, salt, and reserved chile purée in a large bowl with your hands until well incorporated and mixture looks shiny and smooth, about 4 minutes.
Slap the top of masa with the palm of your hand, immediately pulling your hand back. If masa doesn’t stick and your hand looks shiny, the dough is ready. If masa sticks, add another 2 Tbsp. lard and knead until incorporated; repeat slap test. If masa still sticks to your hand, repeat process until you get there (another 2 Tbsp. lard should do it).
For Instant Dry Masa
Mix corn masa flour, stock, lard, salt, baking powder, and ¼ cup reserved chile purée in a large mixing bowl with your hands until dough comes together. Continue to knead until mixture looks smooth and shiny, about 4 minutes.
Slap top of masa with the palm of your hand, immediately pulling your hand back; if dough sticks to your hand, add 2 Tbsp. more lard and knead to incorporate. Repeat slap test. If masa doesn’t stick and your hand looks shiny, dough is ready. If masa sticks, continue adding lard 2 Tbsp. at a time and repeat slap test. Let dough sit 30 minutes, uncovered, until the consistency of peanut butter; it will thicken as it sits.
Soak corn husks in a large bowl of hot water until soft and pliable, about 15 minutes. Using your hands, swirl husks in water to loosen any silks or dirt. Drain, rinse, and shake off excess water.
Place a husk on a work surface and gently stretch out wide end. Measure 5″ wide, then tear off any excess (hold onto the scraps; you’ll use them later). The width doesn’t have to be exactly 5″, but if you go any narrower, your tamale might not cover the filling. This recipe makes about 30 tamales; prep a few extra husks in case some tear.
Arrange husk so wide end is closest to you. Spoon 2 heaping Tbsp. masa onto husk about 4″ from the bottom. Using a putty knife, small offset spatula, or butter knife, spread masa into a thin, even layer, covering the width of the husk and about 5″ up the length of the husk; leave the narrow end uncovered. If you mess up, just scrape off masa and start over. Repeat with remaining husks and masa.
Keeping wide end closest to you, place 2 Tbsp. cold pork filling in the center of masa on each husk, forming a log that runs down the center. Fold 1 side of husk over filling, then fold other side over to cover. Holding tamale seam side up, fold narrow, pointed end of husk away from you and under tamale. Set on a rimmed baking sheet seam side up. Repeat with remaining tamales.
Arrange and Steam the Tamales
Line a large heavy pot with husk scraps. Crumple a large sheet of foil to form a 3″-diameter ball. Place ball in center of pot. Using ball as support, prop tamales upright, with folded end down and seam side facing up, around ball; this will take 4–7 tamales. Continue stacking tamales around the ball, leaning them against one another. Pour broth into pot, being careful not to get any inside tamales (broth should come about ¾” up sides of tamales). Bring liquid to a boil over high heat, then reduce heat to medium-low. Cover pot and simmer tamales, undisturbed, adding more stock as needed to keep some liquid in pot, 40 minutes.
Remove a tamale from pot; let cool 3 minutes. (If you don’t let it rest before checking, masa will stick to husk and appear gummy.) Remove husk; if masa sticks to husk, it’s not ready. Carefully refold and return to pot. Cook 5 minutes more; check again. If husk peels back easily, tamales are done. Remove from heat, uncover, and let sit 10 minutes before unwrapping. Serve with salsa and lime wedges for squeezing over.