Line 2 baking sheets with parchment paper and spray with cooking spray. Set aside.
In a medium bowl, whisk together flour and yeast. Set aside.
In the bowl of an electric mixer, combine milk, butter, sugar, eggs, egg yolks, salt, and vanilla.
Beat to mix.
Add flour mixture.
Knead until dough is smooth and elastic, about 8-10 minutes.
Place in a covered container and proof for 30 minutes.
Turn dough.
Allow to proof for another 30 minutes.
Divide dough into 2 ounce portions.
Roll each portion of dough into a tight ball.
Place seam side down on prepared parchment.
Flatten slightly.
Cover and allow to rise for 45 minutes.
Add 2-3 inches oil to a wide, shallow pot.
Heat oil to 355℉-360℉/179℃-182℃. (Let dough continue to proof while oil heats.)
Fry doughnuts a couple at a time until golden brown and cooked through, about 3-4 minutes, flipping as necessary.
Remove from oil and drain.