Warm the milk in a small saucepan to 105ºF (40.5ºC) to 115ºF (46ºC). Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, stir together the flour, yeast, sugar and salt. Add the warmed milk, vanilla, egg yolks, and butter mixing until the dough is soft and smooth (it will be slightly sticky).
Cover the bowl with plastic wrap and let sit in a warm place to rise for at least 1 hour (and up to overnight).
For the fritters:
In a large sauté pan over medium heat, add the butter and allow to melt. Add the apples, granulated sugar and brown sugar, cinnamon and salt, stirring to combine. Cook, stirring occasionally until the apples are tender and thick syrup forms, about 10 minutes.
Turn the dough out onto a clean, lightly floured surface. Roll the dough out so that it is ½-inch thick. Spread the apple mixture over half of the dough then fold the other half over the top (so that it looks like a calzone).
Use a sharp knife to cut the dough into 1-inch wide strips. Then cut the dough crosswise so the dough forms diamonds. Make sure the apples are well dispersed throughout the dough.
Sprinkle the mixture with flour and shape into a 12-inch by 3-inch rectangle. Divide into 12 equal portions. Shape each portion into a flattened circle and set on a lightly floured baking sheet.
In a heavy bottomed pan or deep fryer, heat enough vegetable oil to reach 2-inches up the pan to 350ºF (180ºC). Working a few portions at a time fry the dough until golden brown on both sides, about 1 to 2 minutes each side.
Remove from the oil and drain on a drying rack with a plate set under it.
For the glaze:
In a medium shallow bowl whisk together the confectioners sugar, apple cider and maple syrup until smooth. Dip each fritter into the glaze and set aside.