Sprinkle the meat on both sides with salt and pepper. Heat the oil and when very hot add the meat. Cook over high heat about 5 minutes. Cook longer if you want medium or well-done meat.
Turn the meat and continue cooking over high heat about 5 minutes, or longer if desired. Remove the meat to a warm platter and keep warm.
Pour off the fat from the skillet. Add the shallots. Add the wine and cook over high heat about 30 seconds. Add the broth and bring to a full rolling boil, stirring to dissolve the brown particles that cling to the bottom and sides of the skillet. Add salt and pepper.
Cook until reduced by half. Meanwhile, blend 2 tsp. of butter and flour in small mixing bowl. Stir it into the simmering sauce and cook briefly. Swirl in the remaining teaspoon of butter. Strain the sauce over the meat and dot the center of each filet with a dab of parsley.
Serve immediately.