Pat the pork shoulder roast dry with paper towels, then generously season all sides with salt and pepper. Heat olive oil in a large skillet over medium-high heat until shimmering. Sear the pork for 2-3 minutes per side until deeply browned—this creates a flavorful crust that builds complexity in the final dish. I find that searing makes a noticeable difference in richness, so I never skip this step. Transfer the seared pork to a plate.

Layer the sliced onion and apple chunks on the bottom of your slow cooker—these vegetables will create a natural bed that prevents sticking and releases their sweetness into the braise. Mince the garlic and scatter it over the vegetables. Place the seared pork from Step 1 on top of this base, skin-side up if the bone-in roast has skin.

Pour the entire 24 oz of sauerkraut with all its liquid over the pork—don't drain it, as that liquid contains tangy flavor that will infuse the meat. If you have fresh thyme, scatter a few sprigs over the top for herbaceous notes. Cover the slow cooker and cook on LOW for 8-10 hours, until the pork is fork-tender and easily shreds. I like to check it around the 8-hour mark; if it's still firm, give it another hour.

Transfer the cooked pork to a cutting board and let it rest for 5 minutes—this makes it easier to shred. Remove and discard any excess fat, then shred or slice the meat into bite-sized pieces using two forks. Return the shredded pork to the slow cooker and gently stir it back into the sauerkraut and braising liquid until well combined. Taste and adjust seasoning if needed before serving.