Dough (First 8 ingredients): In a small saucepan combine the potato, peeled and cut into 1" pieces, with enough water to cover it by 1" and simmer it, covered, for 10 to 15 minutes, or until it is very tender. Drain the potato well, force it through a ricer into a bowl, and stir in 2 Tbsp of the water.

 

In a small bowl proof the yeast in the remaining 1/2 cup water for 5 minutes, or until the mixture is foamy.

 

In a large bowl stir together well the yeast mixture, the mashed potato, the sugar, the butter, the egg, and the salt, add 2-1/2 cups of the flour, and stir the dough until it is combined well.

 

Turn the dough out onto a floured surface and knead it for 8 to 10 minutes, adding as much of the remaining 1/2 cup flour as is necessary to form a smooth and elastic dough.

 

Transfer the dough to a buttered large bowl, turning it to coat it with the butter, let it rise, covered with plastic wrap, in a warm place for 1-1/2 to 2 hours, or until it is double in bulk, and punch it down.

 

The dough may be made 1 day in advance and kept covered and chilled. Bring the dough to room temperature before continuing with the recipe.

 

Preheat the oven to 400 degrees F. Press the dough evenly in a buttered 13" x 9" baking pan and let it rise, covered with a kitchen towel, in a warm place for 30 to 45 minutes, or until it is puffed. Make indentations all over the top of the dough with your thumb and scatter the butter over the dough.

 

Topping (Remaining 3 ingredients): In a small bowl stir together the brown sugar and the cinnamon and sprinkle the mixture evenly over the dough. Bake the cake in the middle of the oven for 20 to 25 minutes, or until it is dark brown and cooked through.

 

Let the cake cool for 5 minutes and cut it into squares.