Heat 2 tablespoons extra virgin olive oil in a heavy bottom pot over high heat. When oil is hot, add 2 pounds stew meat and sprinkle with 3 tablespoons all purpose flour. Meat must be in a single layer and not crowded in order to properly brown, so you may have to work in batches. Cook, stirring only once to turn, until outside starts to brown. Once brown, remove from heat and set aside.
Add 8 ounces mushrooms and 16 ounces pearl onions to pot and allow to cook, stirring infrequently, 3-4 minutes. Add 2 cloves garlic and 2 tablespoons balsamic vinegar, stir, and cook for another 1-2 minutes.
Add 2 cups beef broth and 1 1/2 cups dry red wine and scrape bottom of pan with flat edge wooden spoon to deglaze. Once everything has released from bottom of pan, add browned meat along with any juices, 2 sprigs fresh rosemary, 1 sprig fresh thyme, 2 bay leaves, 1 teaspoon salt, and 1 teaspoon pepper. Stir well.
Reduce heat to a simmer, cover, and cook for at least 1 1/2 hours until meat is tender.
Mix 1 tablespoon corn starch with small amount of cooking liquid in small dish to dissolve. Add slurry back to pot and mix to thicken.