In the meantime, in a large skillet, brown the meat on each side in half of the butter or until the meat is a little more rare than desired. Place on a baking sheet. Garnish with cheese and reserve.
Deglaze the pan with the wine. Add the broth and reduce by half.
In a small bowl, dissolve cornstarch in water. Pour water into the sauce and bring to a boil while stirring. Stir in the rest of the butter. Adjust seasoning.
Place the tournedos in the oven and melt the cheese. Serve with vegetables and the sauce.