In a small bowl, dissolve yeast in the 1/4 cup warm water.
In a small saucepan, combine the 1 cup water, butter, sugar, and salt. Heat and stir just until mixture is warm and butter almost melts. Transfer to a large bowl and stir in yeast mixture.
Using an electric mixer, beat in egg. Beat in as much of the flour as you can with the mixer. Stir in any remaining flour using a wooden spoon. Dough will be moderately soft.
Place dough in a lightly greased bowl. Cover and refrigerate until doubled in size (2 to 3 hours).
Punch dough down. Cover and let rest for 10 minutes. Divide into 24 pieces. On a lightly floured surface, roll each piece into a 10-inch-long rope and tie into a loose knot. Place knotted rolls about 2 to 3 inches apart on greased baking sheets. Cover and let the rolls rise until nearly doubled in size (about 30 minutes).
Bake in a 375 degree F oven 15 minutes or until golden. Remove from oven; brush with melted butter. Serve warm. Or cool; use for chicken salad sandwiches.
Prepare dough as directed. Divide into thirds. Roll each portion into a 20-inch-long rope. Place ropes 1 inch apart on a greased large baking sheet. Starting in the middle, loosely braid to the end. Tuck ends of rope under to seal. Repeat on the opposite end of the loaf. Cover and let rise until doubled in size (about 45 minutes). Bake in a 375 degree F oven 25 to 30 minutes or until bread sounds hollow when you tap it. Cool on a wire rack.