Line up leftover scraps of flaky pastry, pressing them together to make one layer of dough. Roll out into a rectangle one-eighth inch thick. Sprinkle with a thin layer of grated sharp Cheddar cheese, keeping one-quarter inch from all edges. Fold one half of the pastry over the other half and seal the edges. Roll into a rectangle one-quarter inch thick.
To make cheese twists, cut strips four inches long and one-half inch wide. Twist each strip before placing on a cookie sheet. Brush lightly with beaten egg and bake in a hot even (425°F.) for ten to fifteen minutes, until golden brown. Cool.
To make straws, cut strips four inches long and one-eighth inch wide. Place on a cookie sheet. Make rings of pastry two inches in diameter and three-quarters inch wide, using cookie cutters. Place the rings on the cookie sheet. Brush lightly with beaten egg and bake in a hot oven (425°F.) for ten to fifteen minutes, until golden brown. Cool. Place six straws through each ring.