Scald the milk. In a large mixing bowl, combine the scalded milk with the mashed potatoes. Add 1/2 cup sugar plus the margarine. Mix with an electric mixer. If the mixture is still warm, cool to about room temperature before proceeding with next step. - Dissolve the yeast and 1/2 teaspoon sugar in barely warm water. Add to the potato mixture and mix well. Add 2 cups flour and mix again. Cover with a towel and let rise for 25 minutes.
Add the salt and beaten egg to the mixture. Add 4-1/2 cups flour, stirring it into the mixture with a large spoon. Turn onto a well floured board and knead for about 3 to 5 minutes. Add a small amount of extra flour if necessary so the dough can be handled without sticking to your fingers. Grease a large bowl. Place the dough in the greased bowl. Cover with a thin towel, and let rise in a warm, draft free place for about 2 hours or until it is at least double in size.
On a lightly floured surface, roll the dough 3/4" thick. You can use a doughnut cutter to cut the dough or cut as typical Fastnachts - Cut the dough into 3" to 4" wide strips, then cut the strips into 3" to 4" pieces. To allow the center of Fastnacht to fry completely, cut a small slit in the center of each piece, using a sharp paring knife. Arrange the pieces of dough, about 1-1/2" to 2" apart, on large wax paper lined trays. Cover each tray with a thin towel. Place the trays in a warm place for 45 minutes to an hour, or until the dough pieces have raised to about double in size.
Heat the shortening to 365º. Deep fry until both sides are golden brown, turning one time. Drain on white paper towels. Cool completely before serving. Store in a covered, airtight container. Makes about 20 to 24 Fastnachts, depending on size. This recipe can be doubled with no change in preparation directions.
To use this raised doughnut recipe, for glazed doughnuts:
For powdered doughnuts: