In a large bowl, combine the warm milk, sugar, and yeast. Let it sit for about 5-10 minutes until frothy.
Add the melted butter, eggs, and vanilla extract to the yeast mixture. Stir until well combined.
Gradually add the flour and salt to the wet ingredients, mixing until a soft dough forms.
Knead the dough on a floured surface for about 5-7 minutes until smooth and elastic.
Place the dough in a greased bowl, cover with a clean kitchen towel, and let it rise in a warm place for about 1 hour or until doubled in size.
Once risen, punch down the dough and roll it out to about 1/2 inch thick. Cut out circles using a biscuit cutter or a glass.
Place the cut-out dough on a floured baking sheet, cover, and let rise for another 30 minutes.
Heat vegetable oil in a deep fryer or large pot to 350°F. Carefully fry the donuts in batches for about 2-3 minutes on each side until golden brown.
Remove the donuts and place them on paper towels to drain excess oil.
Once slightly cooled, fill a piping bag with your choice of jelly. Poke a hole in the side of each donut and fill with jelly.
Dust the filled donuts with powdered sugar before serving.