To make the filling, cut the cabbages into quaters. STeam until very tender, approvixmately 20 to 30 minutes. Drain and cool. In a strong but thin linen towl, squeeze as much of the liquitd from the steamed cabbage as possible. Squeeze only a small handfull at a time. Discard the juice.
Grind the squeezed cabbbage with the fine blade of a meat gringer. Add the softened cream cheese and butter, and seaon well with salt and pepper, and set aside.
To make the dough, whisk the egg, milk, water, and sour cream together. Add the flour, 1 cup at a time, mixing well after each addition. Turn out onto a floured board and knead until smooth and elastic. This may take about 10 minutes. Add as little additional flour as possible. Put the ball of dough under an inverted bowl until ready to use.
To make the pierogi, but the dough into 1 pieces. On a floured board roll one piece of dough into a large round about 1/16 inch thick. Keep the rest of the dough covered. With a cookie cutter or glass tumbler (21/2 to 3 inches in diamater), cut the dough into rounds. Four each piergi take 1 round of dough streatch it a bit with your fingers, and spoon about 2 tablespoons of the cabbage mixture into the center.
Fold the circle in half and press the edges together. I crimp the edges with my fingertipsinto a decorative pattern. Be sure to seal the edges well or the filling may fall out during the cooking. Put finished dumpling on a towel or tray that has been lightly sprinkled with cornmeal. Continue rolling dough until all the filling has been used up.
Bring a very large kettle of water to the boil. Add 1 tablespoon salt to water and cook about 20 pierogi at one time in simmering water until they are tender and float (5 to 6 minutes). Remove to a serving dish with a slotted spoon and drizzle with melted butter.