Pour boiling water over shortening; stir until shortening is melted. Add 1 cup sugar, salt, and eggs, mixing well. Cool to 105° to 115°.
Dissolve yeast in 1 cup warm water. Add remaining 1/2 teaspoon sugar, stirring well. Combine shortening mixture and yeast mixture in a large mixing bowl; add flour, stirring until smooth. Cover tightly, and refrigerate overnight.
Remove dough from refrigerator; punch down. Turn dough out onto a lightly floured surface, and knead 3 to 4 times. Divide dough into four portions. Roll each portion into a circle about 12 inches in diameter and 1/4-inch thick; cut into 10 wedges. Roll each wedge tightly, beginning at wide end.
Place rolls on greased baking sheets, point side down; curve into crescent shape. Brush tops with melted butter. Cover, and let rise in a warm place (85°), free from drafts, 1 1/2 hours or until doubled in bulk.
Bake at 350° for 20 to 25 minutes or until lightly browned.