To begin, activate the yeast. In a small bowl, dissolve the fresh yeast in warm milk along with 1 teaspoon of sugar. Stir gently and let it sit for 5-10 minutes until frothy. This ensures the yeast is active and ready to leaven the dough.

In a large mixing bowl, combine the flour, remaining sugar, and salt. Add the activated yeast mixture, egg, softened butter, and vanilla extract. Mix the ingredients together until a sticky dough forms. Knead the dough on a lightly floured surface for about 8-10 minutes until smooth and elastic. Cover the dough with a clean cloth and let it rise in a warm place for 1 hour, or until it doubles in size.

After the dough has risen, punch it down gently to release the air. Roll it out on a floured surface to about 1.5 cm (0.6 inches) thick. Use a round cookie cutter or glass (about 7-8 cm in diameter) to cut out circles. Place the circles on a baking sheet lined with parchment paper. Cover them with a cloth and let them rise again for 30 minutes.

While the dough circles are rising, prepare the oil for frying. Heat the vegetable oil in a deep pot or fryer to 175°C (350°F). Use a kitchen thermometer to maintain a consistent temperature, ensuring the Krapfen cook evenly without becoming greasy.

Carefully lower a few dough circles into the hot oil using a slotted spoon. Fry them for 2-3 minutes on each side, or until golden brown. Avoid overcrowding the pot to prevent uneven cooking. Remove the fried doughnuts and place them on a plate lined with paper towels to drain excess oil.

Once the Krapfen are cool enough to handle, fill a piping bag fitted with a narrow tip with jam. Insert the tip into the side of each doughnut and squeeze gently to fill it with jam. Ensure each doughnut has a generous amount of filling without overstuffing.

Dust the filled Krapfen generously with powdered sugar using a fine sieve. This adds sweetness and gives the doughnuts their signature appearance. Arrange them neatly on a serving platter.

Serve the Krapfen warm or at room temperature. Pair them with a cup of coffee or tea for a delightful treat. For an authentic touch, present them on a wooden board or decorative plate. Enjoy them fresh to fully appreciate their fluffy texture and rich flavours.