Combine yeast, 1 teaspoon sugar, and 1 cup lukewarm water in a small bowl; stir well. Let stand 5 minutes.
Combine flour, 1/2 cup sugar, and salt in a large mixing bowl; stir well. Cut in shortening with a pastry blender until mixture resembles coarse meal. Stir in egg. Add yeast mixture and remaining lukewarm water, beating well. Beat at medium speed of an electric mixer 5 minutes. Cover; refrigerate overnight.
Turn dough out onto a lightly floured surface; divide in half. Roll each half into a 30- x 8-inch rectangle. Combine 2 cups sugar, pecans, cinnamon, and butter; sprinkle over rectangles.
Roll up each rectangle, jellyroll fashion, beginning at long side. Cut rolls into 1/2-inch slices; place slices, cut side down, in 2 greased 15- x 10- x 1-inch jellyroll pans. Cover and let rise in a warm place (85°), free from drafts, 30 minutes or until doubled in bulk. Bake at 400° for 12 minutes or until lightly browned. Drizzle glaze over tops of warm rolls, and serve immediately.