Activate the Yeast:

• In a small bowl, combine the warm milk and a teaspoon of sugar. Sprinkle the yeast over the milk and let it sit for about 5-10 minutes until frothy.

Make the Dough:

• In a large mixing bowl, combine the flour, remaining sugar, salt, and vanilla extract. Make a well in the center and add the melted butter, eggs, and the activated yeast mixture. Mix until a dough forms.

Knead the Dough:

• Turn the dough onto a floured surface and knead for about 8-10 minutes until smooth and elastic. You can also use a stand mixer with a dough hook on medium speed for about 5-7 minutes.

First Rise:

• Place the kneaded dough in a greased bowl, cover it with a damp cloth or plastic wrap, and let it rise in a warm, draft-free area for about 1-1.5 hours, or until it doubles in size.

Shape the Berliners:

• After the dough has risen, punch it down and turn it out onto a floured surface. Roll it out to about 1/2-inch thickness. Cut out circles using a round cookie cutter (about 2-3 inches in diameter).
• Place a small spoonful of jam or custard in the center of half of the circles. Top with another circle of dough, sealing the edges by pressing firmly. Place the filled doughnuts on a floured baking sheet.

Second Rise:

• Cover the shaped Berliners with a cloth and let them rise again for about 30-45 minutes, until puffy.

Fry the Berliners:

• In a deep skillet or pot, heat about 2-3 inches of vegetable oil to 350°F (175°C). Carefully fry the Berliners in batches, a few at a time, for about 2-3 minutes on each side until golden brown. Use a slotted spoon to remove them and place them on a paper towel-lined plate to drain excess oil.

Dust and Serve:

• Once slightly cooled, roll the Berliners in powdered sugar. Serve warm or at room temperature.