Dry the beef cubes with paper towels and then sprinkle them with salt and pepper. In batches in single layers, sear the beef in the hot oil for 3 to 5 minutes, turning to brown on all sides. Continue searing until all the beef is browned. Set aside.
Heat the olive oil in a large Dutch oven. Add the beef.
Toss the carrots, and onions, 1 tablespoon of salt and 2 teaspoons of pepper in the fat in the pan and cook for 10 to 15 minutes, stirring occasionally, until the onions are lightly browned. Add the garlic and red pepper and cook for 1 more minute. Add the bottle of wine plus enough beef broth to almost cover the meat. Add the tomato paste and thyme. Bring to a simmer, cover the pot with a tight-fitting lid and place it in the oven for about 2 1/4 hours or until the meat and vegetables are very tender when pierced with a fork.
Combine 2 tablespoons of butter and the flour with a fork and stir into the stew. Add the frozen onions. Saute the mushrooms in 2 tablespoons of butter for 10 minutes until lightly browned and then add to the stew. Bring the stew to a boil on top of the stove, then lower the heat and simmer for 15 minutes. Season to taste.
To serve, toast the bread in the toaster or oven. Rub each slice on 1 side with a cut clove of garlic. For each serving, spoon the stew over a slice of bread and sprinkle with parsley.
