Heat oil in stockpot over medium heat until hot. Place beef Brisket Flat in stockpot; brown evenly. Remove brisket from stockpot; season with salt and pepper, as desired.
Reserve 1/2 cup onion for apples. Add remaining onion and garlic to stockpot. Cook and stir 4 to 5 minutes or until onion is tender. Return brisket, fat-side up, to stockpot. Add cider; bring to a boil. Reduce heat; cover tightly and simmer 2-3/4 to 3-1/4 hours or until brisket is fork-tender.
Meanwhile, heat butter in large nonstick skillet over medium heat until melted. Add apples and remaining onion; cook and stir 5 to 7 minutes or until apples are just tender. Add cranberries and brown sugar; cook 4 to 6 minutes or until cranberries are tender and juices are thickened, stirring occasionally. Stir in walnuts. Keep warm.
Remove brisket; keep warm. Skim fat from cooking liquid. Bring cooking liquid to a boil. Cook, uncovered, 10 to 12 minutes or until reduced by half, stirring occasionally.
Carve brisket diagonally across the grain into thin slices. Serve with reduced cooking liquid and apple mixture.
Nutrition information per serving: 454 Calories; 162 kcal Calories from fat; 18 g Total Fat; 6 g Saturated Fat; 5 g Monounsaturated Fat; 84 mg Cholesterol; 271 mg Sodium; 28 g Total Carbohydrate; 3.7 g Dietary Fiber; 44 g Protein; 4.1 mg Iron; 6.3 mg Niacin; 0.5 mg Vitamin B6; 3.1 mcg Vitamin B12; 10.5 mg Zinc; 44 mcg Selenium;