Place potatoes in a saucepan and cover with water by 1 inch. Bring to a boil over high heat, then reduce heat to a simmer and cook until potatoes are tender and can be mashed. Drain, reserving ½ cup of the potato cooking water, and let cool to lukewarm (no warmer than 110°F).
Mash potatoes (do not add any liquid or seasoning) and measure out ½ cup to use to prepare the Moravian Sugar Cakes. Let potatoes cool slightly.
Dissolve the yeast in warm water in the Cuisinart™ mixing bowl. Insert the flat mixing paddle. Add mashed potatoes, granulated sugar, 2 tablespoons butter, shortening and salt. Mix on speed 1 until smooth and creamy. When lukewarm, add potato water to the yeast mixture. Stir on speed 1 until well blended, about 2 minutes. Lift paddle up from mixer. Cover mixing bowl with plastic wrap and let the mixture rise until “spongy“ in appearance, about 1 to 2 hours.
After dough has risen, while mixing on speed 3, add egg. Scrape bowl and paddle. Mixing on speed 3, add 1½ cups of the flour. When completely mixed in, scrape bowl and paddle. Remove flat mixing paddle and insert dough hook. Add remaining flour ½ cup at a time. This will be a very soft dough. Transfer to a buttered bowl, cover and let rise until double in volume. Punch down and divide dough in half.
Lightly butter one 13x9x2½-inch pan or two 9x9x2½-inch pans. Spread dough evenly prepared pans. Cover with plastic wrap. Let rise until double in volume.
Preheat oven to 375°F. Use fingertips to make holes about ¾ inches apart in rows evenly across the dough. Brush generously with the melted butter. Fill finger holes with dots of butter and sprinkle brown sugar evenly over the top.
Dust with cinnamon if desired.
Bake at 375°F for 20 to 30 minutes. Remove cakes from pans and cool slightly on wire racks. Serve warm for best flavor. Cakes may be frozen (double wrapping suggested) after baking.