Toss potatoes with 1 tablespoon oil, ¼ teaspoon salt, and pepper in a bowl. Cover and microwave, stirring occasionally, until tender (about 5 minutes). Drain well.
Heat 1 tablespoon oil in a Dutch oven over medium heat until shimmering. Brown sausage on all sides (about 5 minutes) and transfer to a plate.
Add onion and remaining ½ teaspoon salt to the Dutch oven, cooking over medium heat until softened (about 5 minutes). Stir in cabbage, cider, grated apple, bay leaves, and thyme. Nestle the sausages into the mixture, cover, and cook until cabbage is tender and sausages reach 160°F (about 20–25 minutes).
Uncover the Dutch oven and simmer until most liquid evaporates (about 2–3 minutes). Transfer sausages to a platter and discard bay leaves. Stir vinegar into vegetables, season to taste, and transfer alongside the sausages. Cover with aluminum foil to keep warm.
Wipe the Dutch oven clean with paper towels. Heat remaining 2 tablespoons oil over medium heat. Add potatoes, cut side down, and cook until browned (2–5 minutes). Transfer potatoes to the platter with sausage and cabbage, garnish with chives, and serve.