Mix 3 cups flour, undissolved yeast, sugar and salt in a large mixer bowl.
Combine milk, water and butter; heat to very warm (120° to 130°F). Butter does not need to melt completely. Add to dry ingredients and beat 2 minutes at medium speed of electric mixer, scraping bowl occasionally. Add 2 cups flour. Beat at high speed 2 minutes, scraping bowl occasionally. Stir in enough additional flour to make a soft dough. Turn out on lightly floured surface and knead until smooth and elastic, about 8 to 10 minutes. Cover; let rest 10 minutes.
Divide dough into 4 equal portions (each is enough to make 1 dozen rolls). Proceed according to directions (below) for desired shapes. Cover; let rise in a warm, draft-free place until almost doubled, about 1 hour.
Bake at 275°F for 20 to 25 minutes, or until rolls just start to change color. Cool in pans or on sheets 20 minutes. Remove from pans or sheets and finish cooling on wire racks. Place cooled rolls in resealable plastic bags and refrigerate up to 1 week OR freeze up to 1 month.
Before serving, preheat oven to 400°F and place rolls on ungreased baking sheet. (Note: if rolls have been frozen, thaw before baking). Bake for 10 to 12 minutes, or until golden brown. If desired, brush hot rolls with melted butter. Serve warm.
Shapes for rolls (each makes 1 dozen rolls):
Classic Dinner Rolls: Divide dough into 12 equal pieces. Shape each piece into a smooth round ball. Place each one in a greased muffin cup OR place all in a greased 9-inch round cake pan.
Cloverleaf: Divide dough into 36 equal pieces. Place 3 each in greased muffin cups.
Bowknots: Roll dough into a 12 x 6-inch rectangle. Cut into 12 (1-inch) strips. Tie each strip in a loose knot. Tuck ends firmly underneath. Place on greased baking sheets about 2 inches apart.
Curliecue Rolls: Roll each piece to a 12 x 9-inch rectangle. Cut into 12 (1-inch) strips. Hold one end of each strip firmly and wind dough to form a coil. Tuck end firmly underneath. Place on greased baking sheets about 2 inches apart.