In mixer bowl, sprinkle yeast over milk and stir with a fork. Let stand until foamy, about 5 minutes.
Attach bowl to mixer fitted with paddle attachment and add egg, egg white, butter, vanilla, 1 cup of the flour, sugar and salt to yeast mixture. Let stand in bowl for 10 minutes. On low speed, mix just until blended, then gradually add just enough of the remaining flour until dough starts to pull away from the sides of bowl. Increase speed to medium and beat for 1 minute.
Transfer dough to a large oiled bowl and cover with plastic wrap. Let rise in a warm, draft free place until doubled in volume, about 30 minutes.
On floured work surface, roll out dough to slightly thicker than 1/4". If dough is tacky, dust with additional flour. Cut dough with cutter into 12 doughnuts, re-rolling scraps as necessary. Place at least 1" apart on prepared baking sheet. Cover with a clean kitchen towel and let rise for 20 minutes.
Meanwhile, in a large, deep pot or deep fryer, heat about 4" oil over medium heat until temperature registers 360*. Deep fry 4 doughnuts at a time in hot oil, turning once with wooden chopsticks until golden brown, about 15 seconds per side. Using a slotted spoon, transfer to paper towels to absorb excess oil. Fry remaining doughnuts, adjusting heat as necessary between batches to maintain oil temperature.
Let doughnuts cool completely then fill with pre-made lemon curd (I purchased Dickenson's) using a pastry bag with a Bismarck or plain tip. If desired, ice with glaze or dust with sugar. (I glazed mine.)