Make the dough: Whisk the egg yolks with vanilla and sour cream, add all the other ingredients, and knead a smooth dough. It will take about 7 minutes with a stand mixer (fitted with a dough hook attachment) or about 12 minutes by hand. The dough should be very smooth.
'Beat' the dough: Roll out the dough slightly (into roughly 8-inch/20cm round/square), fold in half, then fold in half again. Repeat it 4 times. Beat the dough with the rolling pin while you try to roll it out - this will make these crunchy air bubbles on the faworki. You can roll it out with a pasta machine, I usually don't do that - you should beat it with a rolling pin as much as you can. Note: beating the dough is not completely necessary but it will result in a very crispy, delicate dough.
Let it rest: Wrap the dough in plastic foil and leave to rest for 20 minutes (it will be easier to roll out).
Roll out the dough: On a lightly floured surface, roll out the dough as thinly as you can (you should see through the dough). I love to use a silicone rolling mat for rolling out any dough. The dough will be rather tough to roll out.
Cut and shape the faworki: Cut the dough into 1.5-inch (4cm) wide strips (you can use a ravioli cutter wheel or pizza knife). Cut each strip into 5-inch (13cm) long slices (you can cut them parallel to the previous cuts or at an angle, like on the photos). Cut a small slit in the middle of each strip. Twist and pull one end through the slit. Cover the dough with a kitchen towel so it won't dry out.
Fry the dough: Heat 3-4 cups of frying oil to 355°F (180°C) in a shallow pot or a frying pan. You should have about 2 inches of fat in the pot. Fry the faworki in batches until golden on both sides (using two forks, turn them on the other side). Don't go away from the pot, they cook fast - about 1-2 minutes per batch. Don't add too many at once or the temperature of the oil will drop too much and they will soak up the fat. The temperature of the oil should always be between 347°F-365°F(175°C-185°C) - it's best to check it with a candy/grill thermometer.
Dust with powdered sugar: Transfer each batch of faworki to a plate lined with paper towels to drain excess fat. When they are cool enough to handle, transfer them to a second plate and dust them generously with powdered sugar (they should be dusted in sugar while still warm).