In a 4 qt Dutch oven combine stew meat, tomatoes, onion, tomato paste, wine, broth, balsamic vinegar, garlic, salt and pepper. Bring to boiling, reduce heat. Cover and simmer for 1-1.5 hours or until meat is tender, stirring occasionally.
Meanwhile, in a large skillet cook mushrooms in hot oil over medium-high heat for 6-8 minutes or until golden brown, stir occasionally. Stir into cooked meat mixture.
Preheat oven to 400 degrees. Transfer meat mixture to a 3 quart casserole. Prepare cheddar biscuit dough from the center to edges until 1/2 inch thick. Cut 2 inch round circles from the dough, rerolling scraps as needed. Arrange circles over filling. Place on a baking sheet.
Bake uncovered, for 25-30 minutes or until golden brown and edges are bubbly.