Cut the 1.5 lb pork shoulder into 2-3 inch chunks, leaving some fat on the pieces for richness and moisture during cooking. Season generously with salt and pepper on all sides. Place the pork in a slow cooker set to low, cover, and cook for 6-8 hours until the meat is completely tender and easily shreds with a fork. Alternatively, you can braise in a 300°F oven in a covered Dutch oven for 3-4 hours. The low, slow heat breaks down the connective tissue and renders the fat, creating that signature tender, juicy texture of authentic carnitas.
While the pork finishes cooking, prepare all the fresh components. Dice the red onion finely and place in a small bowl. Dice the tomato and place in another bowl. Chop the cilantro and set aside. Thinly slice the radishes and set aside. Cut the lime into wedges and set on a serving plate. I like to slice the avocado just before serving to prevent browning—cut it in half lengthwise, remove the pit, and scoop the flesh into a small bowl, lightly mashing with a fork and a pinch of salt. Once the pork is fall-apart tender, remove it from the cooker and shred using two forks, discarding any large pieces of fat if desired (though some fat adds great flavor). Skim any excess fat from the cooking liquid if preferred, though a little fat contributes to authentic carnitas flavor.
Heat the corn tortillas directly over a gas flame or in a dry skillet over medium-high heat for 15-20 seconds per side until lightly charred and pliable. Stack the warm tortillas in a kitchen towel to keep them soft. To assemble, place 2-3 tablespoons of the shredded pork from Step 1 onto each tortilla, then add a small spoonful of diced red onion, tomato, and radishes. Top with fresh cilantro, a small dollop of mashed avocado, and a splash of salsa verde. I find that building the tacos in this specific order—starting with warm pork, then cold fresh components, and finishing with the creaminess of avocado and brightness of salsa—creates the best balance of textures and flavors. Serve immediately with lime wedges for squeezing over each taco.