Heat 1 1/2 tsp oil in a skillet over medium heat. Add tempeh, and saute 4 minutes or until brown. Stir in soy sauce and 1/2 cup water. Simmer 5 minutes or until liquid has absorbed, turning occasionally. Cool and cut tempeh into small squares.
Heat remaining 1 Tbsp in oil in large skillet over medium heat. Add apples and onion and saute for 12 minutes. Stir in cabbage, sweet cider, vinegar and brown sugar. Reduce heat to medium and partially cover skillet. Cook 25 minutes, or until cabbage is tender, stirring occasionally. Stir in tempeh and chestnuts, season with salt and pepper.