Combine 2 cups flour, sugar, undissolved yeast and salt in a large mixer bowl. Heat milk, water, and 1/4 cup butter until very warm (120° to 130°F). Stir into flour mixture. Beat 2 minutes at medium speed of electric mixer, scraping bowl occasionally. Add egg and 1/2 cup flour; beat 2 minutes at high speed. Stir in enough remaining flour to make a soft dough. Knead on lightly floured surface until smooth and elastic, about 8 to 10 minutes. Cover; let rest 10 minutes. (Or, if desired, place dough in a greased bowl, cover with plastic wrap, and allow to rise in refrigerator for 12 to 24 hours.)
Divide dough in half; roll each half to a 12-inch square, about 1/4-inch thick. Cut each into 6 (12 x 2-inch) strips. Cut each strip into 3 (4 x 2-inch) rectangles. Brush each rectangle with melted butter. Crease rectangles slightly off center with dull edge of knife and fold at crease. Arrange in rows, slightly overlapping, on greased baking sheets, with shorter side of each roll facing down. Allow 1/4-inch of space between each row. Cover; let rise in warm, draft-free place until doubled in size, about 30 minutes.
Bake in preheated 400°F oven for 13 to 15 minutes or until done. Remove from sheets; cool on wire rack. Brush with 1/4 cup melted butter. tip
Use a rolling pin to roll the dough flat before hand rolling your cut-out strips of dough into tight rolls.