In a large Dutch oven or heavy pot, melt butter over medium. Add onion and apple; cook, stirring, until onion softens, 4 to 6 minutes. Stir in red cabbage and season with coarse salt and ground pepper. Add cider vinegar, sugar, and water. Bring to a boil; reduce to a simmer, cover, and cook until cabbage is tender, 20 to 25 minutes. Season with salt, pepper, and sugar.