Add the pork shoulder chunks to your large pot along with the chicken broth, halved onion, garlic cloves, bay leaves, salt, and peppercorns. Bring everything to a boil over high heat, then reduce to a gentle simmer and cover partially. Let this cook for 1.5 to 2 hours until the pork is fork-tender and shreds easily.

While the pork simmers, heat a large dry skillet over medium-high heat. Add the tomatillos, poblano peppers, and jalapeños to the hot pan. Roast them for about 15 minutes, turning occasionally until the skins are blistered and charred in spots.

Transfer the roasted peppers to a bowl and cover with plastic wrap or a kitchen towel for 5 minutes. Remove the stems, seeds, and most of the charred skin from the peppers.

Add the roasted tomatillos, peeled peppers, cilantro, romaine lettuce, cumin, oregano, and 1 cup of the pork broth to your blender. Blend on high speed until completely smooth, about 1 minute.

Once the pork is tender, use tongs to transfer the meat to a cutting board. Fish out and discard the onion halves, bay leaves, and any loose peppercorns from the broth. Shred the pork into bite-sized pieces using two forks, discarding any large chunks of fat.

Pour the blended green sauce through a fine mesh strainer directly into the pot with the broth to catch any remaining seeds or fibrous bits. Use a spoon to press the sauce through the strainer. Bring the mixture to a simmer over medium heat and let it cook for 10 minutes.

Stir in the drained hominy and shredded pork, mixing everything together. Let the pozole simmer for another 15 minutes so the hominy can absorb the flavors of the green sauce. Taste and adjust the seasoning with more salt if needed.

While the pozole finishes simmering, prep all your toppings and arrange them in small bowls. Slice the radishes thin, shred the cabbage, dice the onion and avocado, and cut the limes into wedges. Ladle the hot pozole into large bowls and let everyone customize their serving with their favorite toppings.