In a microwave-safe container, heat the apple cider and butter to warm (120-130 degrees).
Add the vanilla to the butter and apple cider mixture. Set aside for just a moment.
In the bowl of a stand mixer (or large bowl, using a wooden spoon), combine 2 cups of flour, the dry yeast, sugar, salt, and cinnamon.
Add the apple cider mixture to the flour mixture and mix thoroughly.
Add the additional flour and the egg yolks, mixing continually until a soft dough forms (this will take 4-5 minutes).
Remove the dough from the mixer and on a lightly floured surface, knead the dough by hand (for approximately 4-5 minutes) and then place the dough into a lightly greased bowl.
Cover the bowl with plastic wrap and allow the dough to rise until doubled (about an hour and a half) in a warm, draft-free place.
Once the dough has doubled in volume, punch down and allow to rest a few moments.
Divide the dough in half. On a lightly floured surface, roll (or pat) the dough to ½" thickness.
Using a 3" biscuit cutter, cut the dough into circles, and then use a 1" dough cutter to add the center hole to the donuts. OR, use the 1" cutter to strictly make donut holes. Your call.
Allow your donuts to rise again (approximately 45 minutes to one hour) in a warm, draft-free place until they have doubled in size.
In a large deep-sided skillet (or deep fryer), heat roughly 2" of canola oil to 350-degrees on an instant read thermometer.
Carefully use a large slotted spoon or spider to place the donuts 2 or 3 at a time into the hot oil and fry until they're golden brown on each side. Each side will take about 45 seconds (or less). WATCH THEM CAREFULLY! Using the slotted spoon, carefully remove the donuts from the hot oil and place them on a wire rack to cool completely before glazing.