Combine yeast, lukewarm water, and 1 tablespoon sugar in a small mixing bowl; stir well. Let stand 5 minutes.
Combine 1/4 cup plus 3 tablespoons sugar, 1/2 cup scalded milk, shortening, and salt in a large mixing bowl; cool to lukewarm (105° to 115°). Add eggs and 2 cups flour; stir until well blended. Stir in yeast mixture; add enough remaining flour to make a soft dough. Cover and let dough rest 10 minutes.
Turn dough out onto a floured surface, and knead 10 minutes. Shape dough into a ball; place in a lightly greased bowl, turning to grease top. Cover and let rise in a warm place (85°), free from drafts, 1 1/2 hours or until doubled in bulk.
Punch dough down; let rest 10 minutes. Turn dough out onto a lightly floured surface; divide dough into 4 equal portions. Roll each portion into a 12- x 6-inch rectangle; brush with butter, leaving a 1-inch margin on all sides.
Combine remaining 1 cup sugar and cinnamon; sprinkle over each rectangle of dough. Roll up jellyroll fashion, beginning at long side; moisten edges with water to seal.
Cut rolls into 1-inch-thick slices; place slices, cut side down, in four 8-inch round cake pans. Cover and repeat rising procedure 45 minutes or until doubled in bulk.
Bake at 350° for 20 minutes or until lightly browned. Combine powdered sugar, 3 tablespoons milk, vanilla, and pecans in a small bowl; mix well. Drizzle over warm rolls, and serve.