Place the potato in a small saucepan, cover with water to a depth of 1", and simmer, covered, until tender, 10 to 15 minutes.

Drain well, reserving the cooking water.

Force the potato through a ricer into a small bowl or mash as smooth as possible with a fork.

Measure out 1 cup of gently packed potatoes into a small bowl, and stir in 2 tablespoons of the reserved cooking water.

Cover and keep warm.

In a glass measuring cup, dissolve the yeast and ½ teaspoon of the sugar in ¼ cup of the reserved potato water.

Let stand until the mixture bubbles up, 5 minutes.

3.

Combine the potatoes, the remaining 1 cup sugar, the shortening, ¼ cup butter, and salt in a large mixing bowl, and beat with an electric mixer on medium speed until the shortening melts, 2 minutes.

Stir in the yeast mixture and beat on low speed for 30 seconds.

Cover with a kitchen towel and let rise in a warm place (80° to 85°F), free from drafts, until spongy, 1½ hours.

Stir in the eggs and flour to make a soft dough.

Shape the dough into a ball.

Place in a greased bowl, turning to grease the top.

Cover with plastic wrap and let rise in a warm place, free from drafts, for 2 hours.

The dough will increase in size by one half.

Turn the dough out onto a lightly floured surface and knead until it is smooth and elastic, 5 minutes.

Pat the dough evenly into a greased 13" × 9" baking pan.

Cover with plastic wrap and let rise in a warm place, free from drafts, 45 minutes to an hour.

Place a rack in the center of the oven, and preheat the oven to 375°F.

With your thumb or the end of a wooden spoon, deeply dimple the dough.

Tuck the slices of butter into the dimples and over the top of the dough.

Place the brown sugar and cinnamon in a small bowl and stir to combine; sprinkle this evenly over the dough and down into the dimples.

Place the pan in the oven, and bake until the cake is well browned and cooked through, 25 to 30 minutes.

Let cool for 30 minutes in the pan before serving.