Mix 3 1/2 cups flour, yeast, sugar, and salt in large bowl. Melt 4 tablespoons butter; cool until warm. Mix with milk and egg; stir into flour.
Knead 8 to 10 minutes until smooth and elastic, using 2 tablespoons extra flour only as needed against sticking. Cover; rise 60 to 90 minutes until nearly doubled, additional to active prep time.
Grease 9-by-13-inch metal pan with 1 tablespoon butter. Roll dough into 12-by-16-inch rectangle; brush with 2 tablespoons melted butter.
Cut sixteen 3-by-4-inch rectangles. Fold crosswise almost in half, leaving narrow lower lip visible. Arrange closely; cover and rise 35 to 50 minutes until puffy.
Heat oven to 375°F; bake 18 to 22 minutes until golden and cooked through. Brush with remaining tablespoon butter; cool 10 minutes before separating.