Heat oil in large stockpot over medium heat until hot. Brown beef Short Ribs on all sides. Season with salt and pepper as desired. Add broth, 1 cup wine, onions, garlic and thyme to stockpot; bring to a boil. Reduce heat; cover tightly and simmer 1-3/4 to 2-1/2 hours or until beef is fork-tender.
Remove Short Ribs from stockpot; keep warm. Strain vegetables and skim fat from cooking liquid. Reserve 3/4 cup cooking liquid for sauce; discard remaining cooking liquid.
Melt 1 tablespoon butter in large nonstick skillet over medium heat. Add mushrooms, shallots and minced thyme; cook and stir 5 minutes or until mushrooms are tender. Dissolve remaining 1/2 cup red wine in cornstarch. Add reserved cooking liquid and cornstarch mixture to skillet. Bring to a boil. Reduce heat and simmer 5 minutes; stirring often. Remove skillet from heat; stir in remaining 1 tablespoon butter. Serve sauce over Short Ribs.
Nutrition information per serving: 314 Calories; 151.2 kcal Calories from fat; 16.8 g Total Fat; 7.7 g Saturated Fat; 0.2 g Trans Fat; 1 g Polyunsaturated Fat; 6.6 g Monounsaturated Fat; 71 mg Cholesterol; 237 mg Sodium; 7.6 g Total Carbohydrate; 0.9 g Dietary Fiber; 1.9 g Total Sugars; 22 g Protein; 0 g Added Sugars; 24.6 mg Calcium; 2.6 mg Iron; 357 mg Potassium; 9.1 IU Vitamin D; 0.2 mg Riboflavin; 3.2 mg Niacin; 0.3 mg Vitamin B6; 2.3 mcg Vitamin B12; 192 mg Phosphorus; 5.3 mg Zinc; 17.1 mcg Selenium; 85.3 mg Choline;