Combine yeast, 1 teaspoon sugar, and 1 cup lukewarm water in a small mixing bowl; stir well. Let stand 5 minutes or until bubbly.
Combine 1 cup boiling water, shortening, remaining 1/2 cup sugar, and salt in a large mixing bowl. Stir until shortening melts and sugar dissolves; let mixture cool to lukewarm (105° to 115°). Stir in yeast mixture and egg, mixing well.
Combine flour in a medium mixing bowl; stir well. Gradually add 2 1/2 cups flour mixture to yeast mixture; beat at low speed of an electric mixer until dough is smooth. Stir in remaining flour mixture to make a soft dough.
Place dough in a greased bowl, turning to grease top. Cover and refrigerate overnight.
Punch dough down. Shape dough with well-greased hands into 1-inch balls; dip each ball in melted butter. Place in lightly greased muffin pans using 3 balls in each muffin cup. Sprinkle graham cracker crumbs evenly over tops of rolls. Cover and let rise in a warm place (85°), free from drafts, 1 hour or until doubled in bulk.
Bake at 375° for 15 minutes or until lightly browned. Serve warm.