In the bowl of a stand mixer, combine flour, yeast, baking powder, sugar, and salt.
With mixer running, add milk, eggs, vanilla, and butter.
Mix on low speed for 1-2 minutes, until combined.
Switch to dough hook.
Turn speed to medium and knead for 8-10 minutes, until dough is smooth.
Turn dough into covered, oiled container.
Allow to rise for 1 hour.
Turn dough out onto floured surface.
Sprinkle top of dough with flour.
Roll to ½ inch thick.
Cover dough and let rest for 10 minutes.
Cut out doughnuts.
Place on parchment lined pans that have been lightly sprayed with cooking spray.
Cover and let rise 15 minutes.
While dough is rising, heat 2 inches of oil in a large pot to 350℉/177℃.
Fry doughnuts in small batches, 2 or 3 at a time, 1-2 minutes on each side until golden brown.
Drain on paper towels.