In a large skillet with a tight-fitting lid, heat the olive oil over medium-high heat until it shimmers and is hot. Carefully add the sausage and reduce heat to medium. Cook, turning occasionally, until browned and fully cooked. Transfer the sausage to a plate.
Add wine (or beer) to skillet and scrape any brown bits from the bottom of the pan (the liquid with boil off. that's ok). Add a small splash of oil to the pan along with the onions, garlic, and carrots. Mix well. Sauteé for approximately 3-4 minutes, stirring occasionally. Stir in the cauliflower florets, salt, pepper, and dried thyme. Mix well and cover with lid. Continue to cook over medium heat for approximately 15-20 minutes, stirring occasionally, or until carrots and cauliflower just start to soften.
Add the apples to the skillet and mix well. Cover again and cook for an additional 2 minutes before adding the cabbage and fresh thyme. Mix and cook for 1-2 minutes more. Taste for salt and season as you see necessary. Continue to cook until vegetables reach desired tenderness.