Jelly Doughnut Holes
For the doughnuts, put the flour into a bowl, make a well in the center and add in the yeast. Sprinkle about 1 teaspoon of sugar into well along with some water and mix to form a dough using a fork to form a slurry. Cover the bowl and let rise for about 15 minutes in a warm place, until bubbles rise from the dough.
Work the dough slightly with some flour (using a hand mixer with dough hooks if desired). Then add in the remaining sugar, egg, vanilla sugar, grated lemon zest and salt and work together with a little water. Add enough water that a flexible, well-kneadable dough forms. Knead the dough well until the bubbles disappear, sprinkle with a little water, cover and let rise to double the size for about 30 minutes.
Roll out the dough onto a floured surface until about 1.5 cm (approximately 0.5 inch) thick in the shape of a rectangle. On one half of the dough use doughnut cutters to mark 3-5 cm (approximately 1-2 inch) diameter circles.
In the middle of these circles, put about a small dollop of the cranberry jam. Then place the other half of the dough on top, press it down slightly around the filling and cut out the holes. Reshape these slightly with your fingers. Cover the doughnuts on a lightly floured surface and let rise again until they have risen by about half.
Meanwhile heat the oil for frying in the deep fryer to 170°C (approximately 340°F), or fill up a wide pot about 5 cm (approximately 2 inches) deep with the oil and heat. Dip a wooden spoon into the oil to check if the temperature is correct. When small bubbles form on the spoon, the oil has reached the right temperature.
Carefully place small batches of the doughnuts into the oil using a slotted spoon and fry until golden brown, about 7 minutes. Remove the finished doughnuts with the slotted spoon, and drain well. Let cool spaced apart from each other, and sprinkle with powdered sugar. Serve immediately.