Heat olive oil in a skillet over medium-high heat. Add turkey sausage and cook until browned, breaking it into small crumbles with a spatula. Drain any excess fat.
Transfer the browned sausage to a 6-quart slow cooker.
Add the cubed butternut squash, diced onion, minced garlic, dried sage, and dried thyme to the slow cooker.
Pour the chicken bone broth over the ingredients and stir to combine.
Cover and cook on Low for 6 hours (or High for 3 hours) until the butternut squash is fork-tender.
Optional: Remove two cups of the squash and broth (avoiding the sausage), blend until smooth, and return to the pot for a creamier consistency.
Stir in the Greek yogurt until fully incorporated to increase protein and creaminess.
Season with salt and pepper to taste and serve immediately.