Season the pork shoulder thoroughly with cumin, garlic powder, sea salt, and black pepper.
Place the seasoned pork in a slow cooker and cook on low for 8 hours until the meat is tender and easily pulls apart.
Remove the pork from the slow cooker and shred it using two forks, removing any large pieces of visible fat.
Heat the avocado oil in a cast-iron skillet over medium-high heat.
Add the shredded pork to the hot skillet in a single layer and press down firmly, searing for 3-4 minutes until the bottom is crispy and golden.
While the pork crisps, toss the shredded cabbage with lime juice in a small bowl to create a bright, crunchy slaw.
Warm the corn tortilla in a dry skillet or directly over a gas flame for 30 seconds per side.
Assemble the taco by filling the tortilla with the crispy carnitas, topping with the lime slaw, and finishing with a dollop of Greek yogurt.