In large nonreactive flameproof casserole, melt butter over moderately high heat. Add onion and saute until softened but not browned, 3 to 4 minutes. Add garlic and cook 1 minute more.
Add cabbage and toss. Cover and cook, stirring occasionally, until cabbage wilts slightly, about 3 minutes.
Add apples, vinegar, sugar, mustard seeds, salt and pepper. Toss well and continue to cook, stirring often, until apples are tender, about 8 minuts.
Note: This recipe can be made up to 3 days in advance. Cover and refrigerate. Reheat before serving.
This piquant red cabbage with green apples is a classic combination that has a tart fruitiness.