Mix meat, onion, rice, parsley, mint, oregano, dill, egg, butter, salt and pepper.
Rinse grape leaves in cold water to wash away brine.
Place 2 tsp filling in the center of 1 grape leaf and roll leaf around the filling, tucking the ends of the leaf in. Continue with additional leaves until all the filling is used.
Line the bottom of a casserole pan (one with a lid) with grape leaves. Arrange the dolmathes side by side and in layers. Place a heavy plate on top of the dolmathes to keep them in place.
Combine beef broth, tomato paste and enough water to just cover the dolmathes. Pour over the dolmathes. Cover the casserole with lid and simmer on the stove top until the rice is tender- approx 30- 40 minutes.
Make a paste out of the lemon juice and flour. Set aside.
Beat egg yolks and blend in the lemon paste.
Beat the egg whites until stiff. Slowly add the yolk/lemon paste mixture and 1 cup of liquid from the dolmathes pot. Cook over medium low heat for 5 to 10 minutes (stirring constantly) until sauce is thick enough to coat the back of a spoon. If sauce is too thick- thin with a little more of the dolmathes cooking liquid.