Heat olive oil in a large pot over medium heat. Add the sausage and cook until browned, breaking it up with a spoon, about 5-7 minutes.
Add the diced onion and cook until softened, about 3-4 minutes. Stir in the minced garlic and cook for an additional minute until fragrant.
Add the cubed butternut squash, chicken broth, thyme, oregano, salt, and pepper. Bring to a boil, then reduce heat and let simmer for 20-25 minutes, or until the squash is tender.
If using kale, stir it in during the last 5 minutes of cooking.
Remove from heat and stir in the apple cider vinegar. Adjust seasoning if necessary.
Serve hot, garnished with fresh herbs if desired.