1. Place the potato in a small saucepan, cover with water and simmer, covered, for 15 minutes or until tender. Drain well, reserving the cooking water. Mash the potato as smooth as possible with a fork, food mill, or ricer.
2. Measure out 1 cup of potatoes into a small bowl and stir in 2 tablespoons of the potato cooking water. Cover and keep warm.
3. Dissolve the yeast and ½ teaspoon sugar in ¼ cup warm potato water; let stand 5 minutes, or until mixture bubbles. Discard any remaining potato cooking water.
4. Stir together the warm mashed potato, the remaining 1 cup sugar, the shortening, ¼ cup butter, and salt in a large mixing bowl; stir until melted. Stir in the yeast mixture. Cover and let rise in a warm place for 1½ hours, or until spongy.
5. Stir in the eggs and flour to make a dough. Shape the dough into a ball. Place in a greased bowl, turning to grease the top. Cover with a cloth or plastic wrap misted with nonstick spray and let rise in a warm place for 2 hours, or until doubled in bulk. Turn the dough out onto a lightly floured surface; knead 5 minutes or until smooth and elastic.
6. Pat the dough evenly in a greased 9×13-inch baking pan. Cover and let rise in a warm place for 2 hours, or until doubled in bulk. P
7. Preheat the oven to 375°. Deeply dimple the surface of the dough with your thumb or the end of a wooden spoon. Tuck a butter cube into each dimple.
8. Stir together the brown sugar and cinnamon in small bowl; sprinkle evenly over the dough and down into the dimples.
9. Bake in center of oven for 20 minutes, or until browned and cooked through. Let cool 5 minutes before serving.