Add the carrots, parsnips, sweet potato, and onion to the bottom of the slow cooker. Spread them into an even layer.
Place the pork shoulder on top of the vegetables. Sprinkle the salt and pepper over the pork.
Scatter the minced garlic and thyme sprigs around the pork.
Pour the apple cider over everything, making sure it reaches the bottom of the pot.
Cover and cook on low for 8 hours. The pork should pull apart easily with a fork when done.
Remove the thyme sprigs before serving. Slice or shred the pork and serve it with the vegetables and some of the cooking liquid.