Combine 2 cups flour, sugar, 2 teaspoons salt, and yeast; stir. Combine milk and 1/4 cup butter in a saucepan; heat until butter melts, stirring occasionally. Cool to 120° to 130°. Add liquid mixture to flour mixture, beating at low speed of an electric mixer. Beat 2 minutes at medium speed. Stir in enough of the remaining 4 cups flour to make a soft dough.
Sprinkle 1/4 cup flour over work surface. Turn dough out; knead until smooth and elastic (about 10 minutes). Place in a greased bowl, turning to grease top. Cover and let rise in a warm place (85°), free from drafts, 45 minutes or until doubled.
Position knife blade in food processor bowl, and add parsley, onions, and garlic. Process 20 seconds. Add remaining 1/2 cup butter, remaining 1/2 teaspoon salt, and pepper; process 15 seconds.
Punch dough down; divide in half. Sprinkle 1 tablespoon flour over work surface. Roll 1 portion into a 16- x 10-inch rectangle. Spread half of parsley mixture over dough, leaving a 1-inch border. Roll up dough, starting at long side. Pinch seam and ends to seal. Repeat procedure.
Place loaves, seam side down, on a greased baking sheet. Make 1/4-inch-deep slits in each loaf. Cover and let rise in a warm place, free from drafts, 20 minutes or until doubled. Combine egg and water; brush over loaves. Bake at 375° for 30 minutes or until loaves sound hollow when tapped.