Heat the olive oil in a large skillet over medium heat.
Add the sliced apple chicken sausage to the skillet and cook for 5-6 minutes, stirring occasionally, until browned on all sides. Remove the sausage from the skillet and set aside.
In the same skillet, add the diced onion and cook for 3 minutes until softened.
Add the minced garlic and cook for 30 seconds until fragrant.
Add the sliced carrots, diced red bell pepper, diced apple, halved Brussels sprouts, and diced zucchini to the skillet. Stir to combine.
Sprinkle the dried thyme, ground cinnamon, ground nutmeg, salt, and black pepper over the vegetables. Stir well to evenly coat.
Pour the chicken broth into the skillet and stir to deglaze the pan, scraping up any browned bits from the bottom.
Cover the skillet with a lid and cook for 10 minutes, stirring halfway through, until the vegetables are tender.
Return the browned apple chicken sausage to the skillet and stir to combine with the vegetables.
Cook uncovered for an additional 3-4 minutes to heat the sausage through and allow any excess liquid to evaporate.
Taste and adjust seasoning with additional salt and pepper if needed.
Serve warm directly from the skillet.