Preheat oven to 250 degrees.
Dry the beef cubes with a paper towel and then sprinkle with salt and pepper. Heat the olive oil in a large Dutch oven. In single layer batches, sear the beef in the hot oil for 3 to 5 minutes, turning to brown on all sides. Remove the seared cubes to a plate and continue to sear the remaining meat until all is browned. Set aside.
Pour the carrots and onions in the Dutch oven and sprinkle with another pinch of salt and pepper. Stir and cook over medium heat for 10-12 minutes until the onions are lightly browned. Add the garlic an cook for 1 more minute.
Add the potatoes to the pot, and then immediately add the tomato paste. Stir constantly until the past turns a pretty burgundy color, about 2 minutes.
Pour in the meat and reserved juices, along with the entire bottle of red wine and 3 of the cups of beef broth.
Bring mixture to a boil, stiffing occasionally. Once the stew comes to a boil, cover and place in the bottom third of the oven. Cook for about an hour and 15 minutes or until the meat and potatoes are very tender when pierced with a fork.
Meanwhile, in a salute pan, add the butter, worcestershire sauce and the mushrooms. Sprinkle with a pinch of salt and pepper. Stir carefully, until the mushrooms are cooked through, about 6 minutes. Remove the pan from heat.
With the remaining 1/2 cup beef broth, whisk in the cornstarch until there are no lumps and the mixture is smooth.
Once the meat and vegetables are very tender, remove the stew from the oven. Carefully remove the hot lid. Add the mushrooms with the pan juices, and the beef broth/cornstarch mixture.
Place over medium heat and stir combing all ingredients and until the stew has thickened slightly, about 10 minutes. Add more beef broth if necessary.
Ladle into bowls and serve hot.
Can be frozen for up to 6 months.