French Style Braised Short Ribs

INGREDIENTS:

2 pounds beef short ribs, cut into 3-4 inch pieces
1 large onion, sliced
3 carrots, sliced
3 stalks celery, sliced
8 ounces mushrooms, quartered
4 cloves garlic, chopped
1 pinch red pepper flakes (optional)
3 cups beef broth
2 cups dry red wine (or more broth)
2 tablespoons tomato paste
2 heads of garlic, with the tops removed
2 tablespoons balsamic vinegar
2 bay leaves
1 teaspoon thyme, chopped (or 1/2 teaspoon dried thyme)
1 teaspoon rosemary, chopped (or 1/2 teaspoon dried rosemary)
2 tablespoons parsley, chopped

DIRECTIONS:

Brown the beef in a large, oven-safe, sauce pan over medium-high heat, about 3-4 minutes per side, and set aside before draining off all but 2 tablespoons of the grease.
Add the onions, carrots, celery, and mushrooms and cook until tender, about 7-10 minutes.
Add the garlic and red pepper flakes and cook until fragrant, about a minute …