Combine 2 cups flour, undissolved yeast, sugar, salt and cinnamon in the bowl of a stand mixer fitted with a dough hook. Mix on low just until yeast is evenly distributed.
In a saucepan on the stovetop heat milk and butter to very warm (120°F to 130°F). Remove from heat and add vanilla, mix well.
Add to flour mixture in mixing bowl with egg yolks. Beat for 2 minutes at low speed. Continue adding remaining flour until soft dough forms.
Knead for 4-6 minutes until the dough is smooth and elastic. (You can also do this by hand.) Cover and let dough rest for 10 minutes.
Roll out dough on a lightly floured counter into a 12-inch circle, about 1/2-inch thick. Using a 3-inch doughnut cutter or a cookie or biscuit cutter, cut out as many rounds as possible. Cut out center with a 1-inch cookie cutter.
Place doughnuts about 3 inches apart on a large lightly greased or parchment lined baking sheet. Re-roll and cut remaining dough. Cover doughnuts and let rise for 45 minutes to 1 hour. (The doughnuts will rise and expand, allow enough room so they don't touch)
To fry: Heat at least 2-3 inches of oil in a deep fryer or deep pan to 350°F. Fry 2 to 3 doughnuts at a time, turning occasionally until evenly browned, about 2 to 3 minutes. Remove from oil and drain on a paper towel lined baking sheet. Cool a few minutes, then transfer to wire rack. Dunk the doughnuts in the glaze place back onto a cooling rack. Serve warm or at room temperature.
To bake: Preheat oven to 375°F. Brush doughnuts on all sides with melted butter and arrange on a sheet pan sprayed with cooking spray, without touching. Bake for 8 to 10 minutes or until puffed and golden. Dip in glaze.
To make the glaze: Bring apple cider to a boil in a small saucepan. Lower the heat to medium and cook until it's reduced in half, about 6-8 minutes. Place powdered sugar in medium bowl. Whisk in hot cider and corn syrup until smooth. Dip doughnuts into glaze.