Heat the olive oil in a large skillet over medium-high heat. Add the pork shoulder pieces and sear until browned on all sides, about 6 to 8 minutes total.
Add the diced onion and minced garlic to the skillet. Cook for 2 minutes until the onion softens slightly.
Transfer the pork, onion, and garlic to a slow cooker. Pour in the apple cider and chicken broth.
Add the butternut squash cubes, chopped sage, salt, and black pepper. Stir gently to combine.
Cover and cook on low for 7 to 8 hours until the pork is very tender and the squash is soft.
Taste and adjust salt if needed before serving.