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