In a large mixing bowl, combine the flour, sugar, instant yeast, and salt, then add a warmed mixture of milk and butter, followed by eggs and vanilla.

Turn the dough onto a floured surface and knead for about 10 minutes until smooth and elastic.

Shape into a ball, place in a greased bowl, cover with a damp cloth, and let rise in a warm area for 1 to 2 hours.

Punch down the risen dough, roll it out to ½ inch thick, and cut out circles using a doughnut cutter.

Cover shaped doughnuts lightly and let them rise again for 30 to 45 minutes.

Heat oil to 350°F, fry doughnuts until golden brown on both sides, then drain on paper towels.

Fill each cooled doughnut with pastry cream using a piping bag, and dust with powdered sugar before serving.