Heat oil in a Dutch oven or large pot over medium-high heat. Coat beef cubes with flour, shaking off the excess. Fry beef cubes until browned on all sides. Remove from the pot. Add the onion, mushrooms, and garlic to the pot, and cook stirring constantly until onion is tender, about 3 minutes.
Return beef to the pot, and stir in tomato paste, beef broth, and beer. Add potatoes and carrots, cover, and simmer over low heat for about 1 hour. Mix together the cornstarch and cold water. Stir into the stew, and simmer until thickened. Sprinkle with parsley and serve.