Proof the yeast by combining it with the lukewarm milk and about 2 tablespoons of sugar. Mix well and place in a warm spot for 20 minutes. The yeast should become active and foam up, becoming what is called a sponge.
While the yeast is doing its thing, combine the rest of the ingredients and whip til fluffy. Combine the yeast sponge with the flour and mix up a little. Add the egg mixture and mix well. Knead by hand for about 10 minutes or use a mixer with dough hooks for 5 minutes.
Form a ball with the dough and leave it in the bowl. Cover with a clean kitchen towel and put in a warm place (about 85 degrees F) to rise for 20 minutes. If your kitchen is cold, warm the oven to 85 degrees F (30 C) and place the dough in there.
Punch the dough down and knead by hand on floured board for about 5 minutes. Sprinkle with more flour and work it in by increments if dough sticks to your hand. Add milk by tablespoons if the dough is too dry and hard to knead.
Form a ball and return the dough to the bowl. Cover with the towel and return to the warm spot for 60 minutes to rise a second time.
Turn the dough onto a floured board and punch down again.
Now there are two ways to proceed: One is to form balls with the dough that are about 2 inches in diameter. Roll the balls between your palms to eliminate any seams or folds. Seams and folds "bloom" in the oil and result in a misshapen Krapfen. Two is to press the dough into a flat sheet about 1/2 inch thick. Let it rest for about 10 minutes then use a cookie cutter or rim of a drinking glass to cut 4-inch disks. Reform leftover dough into a flat sheet and cut more disks until most of the dough is used up.
Whether you form ball or disks, place the dough shapes on greased and floured sheets. Cover the dough with the kitchen towel and return to the warm place for another 30 minutes.
Meanwhile bring a pot with 2-3 inches of oil, shortening or lard (old school, German style) to 338 degrees F (170 C). Carefully remove a ball or disk, whatever you decided, turn it over and place gently into the oil, bottom up.
Fry 1-2 minutes then turn the donuts over and fry an equal amount of time on the other side. Properly risen dough should be so light that the donuts float, resulting in a white band around the middle. No white band means dense, overcooked donuts.
Remove from oil to a plate lined with paper towels.
There are two ways to glaze the Krapfen: One, roll the still-warm Krapfen in a plate of sugar. Two, sprinkle with powdered sugar, BUT WAIT UNTIL AFTER YOU FILL THEM.
To fill: Load a baking syringe with jam and inject each donut with about 2 teaspoons of the sweet stuff. Then sprinkle with powdered sugar on both sides if you waited for that.