Combine the yeast and water in a small bowl. Stir together and set aside.
In a large bowl cream the shortening, ¼ cup butter, and sugar together. Gradually beat in boiling water.
Add yeast mixture and beat until well blended. Add the egg and mix well.
Add the flour and salt and mix together well. Cover bowl with plastic wrap and refrigerate until ready to use.
Three hours before ready to use, roll dough out on a floured surface so that it is ½-inch thickness. Using a small round biscuit or cookie cutter (2 to 2 ½-inches) cut dough into circles and fold each circle in half. Place on large greased baking sheets and brush with melted butter. Cover baking sheets with a tea towel and let rise in a warm place for 2 ½ hours.
Preheat oven to 400 degrees. Bake rolls for 5 to 7 minutes, until golden brown.