While you're organizing your workspace, prepare all your toppings ahead of time so they're ready when the pork finishes cooking. Dice the white onion into 1/4-inch pieces, chop the cilantro, dice the tomato, and slice or mash the avocado (save this for last to prevent browning). Cut the lime into wedges and set out your corn tortillas. Now season the pork shoulder chunks generously with kosher salt and ground cumin, making sure every piece is well coated—this allows the seasoning to penetrate during the long, slow cooking process.
Place the seasoned pork chunks in a slow cooker (or a Dutch oven in a 300°F oven) with just enough water to barely cover the meat—about 1 to 1.5 cups. I prefer the oven method because it gives the pork a slight caramelization on top that adds depth to the flavor. Cook on low for 4-5 hours until the meat is fall-apart tender and shreds easily with a fork. For a richer result, you can drain the liquid and finish the pork uncovered in a 400°F oven for 15-20 minutes to develop a light crust.
Remove the cooked pork from the heat and use two forks to shred it into bite-sized pieces. Warm your corn tortillas directly over a gas flame or in a dry skillet for about 30 seconds per side until they're pliable and slightly charred. Place a generous handful of shredded pork onto each tortilla, then top with a small handful of diced onion, followed by salsa verde. I like to add the salsa while the pork is still warm so it soaks into the meat slightly. Top with diced tomato, fresh cilantro, and avocado slices.
Serve the tacos immediately while the pork is still warm and the tortillas are soft. Squeeze fresh lime juice over each taco just before eating to brighten all the flavors—the acidity ties everything together beautifully.