Step 1

Filling: Using a paring knife, scrape out the vanilla seeds. Place half of the pod, half of the seeds, and 2 tablespoons butter in a 12-inch skillet; set over medium-high heat. Cook until butter is bubbling. Add half of the apples; toss to coat. Add 1/4 teaspoon cinnamon and 2 tablespoons sugar; saute, stirring occasionally, until apples begin to soften, about 5 minutes. Add 2 tablespoons vinegar and 1/2 cup cider; increase heat to high. Cook until liquid has been absorbed and apples start to brown, about 8 minutes. Remove from heat. Remove and discard pod. Transfer apples to a baking sheet. Wash skillet, and repeat with the remaining ingredients.

Step 2

Dough: Place yeast in the bowl of an electric mixer. Heat milk in a pan over medium heat until warm to the touch. Pour milk over yeast; sprinkle 2 cups pastry flour on top. Set aside until flour begins to crack, 15 to 20 minutes.

Step 3

Place the egg yolks and sugar in a medium bowl; whisk to combine. Add the cider, butter, salt, cinnamon, vanilla extract, the remaining 1/4 cup pastry flour, and 1 cup bread flour; whisk to combine.

Step 4

Add flour mixture to the yeast mixture. Using the dough-hook attachment, mix on low speed 30 seconds. (The dough should look very soft but still have structure; if it appears liquidy, add remaining 2 tablespoons bread flour.) Increase speed to medium and mix dough 3 to 4 minutes.

Step 5

Lightly oil a large bowl. Sift an even layer of pastry flour onto a clean work surface, and lightly flour your hands. Turn out dough, and gather into a ball. Transfer dough to oiled bowl, and cover with plastic wrap. Set aside in a warm place to rise until doubled in size, about 1 1/2 hours.

Step 6

Lightly dust a baking pan with flour, and line a second one with paper towels. Set both pans aside.

Step 7

Turn out dough onto a lightly floured work surface. Using your hands, stretch the dough into a 10-by-15-inch rectangle, about 1/2 inch thick. Spread half of the reserved apple mixture over dough, and fold dough, like a letter, into thirds. Pat down with your hand, forming another 10-by-15-inch rectangle. Spread the remaining apples over the dough, and fold into thirds again; the apples will be evenly distributed throughout the dough. Gather the dough into a ball, and return dough to oiled bowl. Re-cover, and set aside in a warm place until doubled in size again, about 30 minutes.

Step 8

Turn out dough onto a lightly floured work surface; pat into a 10-by-15-inch rectangle, about 1 inch thick. Using a 2 1/2-inch round cutter, cut out fritters as close together as possible, dipping cutter in flour before each cut. Transfer fritters to floured baking pan. Set aside to rest 10 minutes, but not longer.

Step 9

While dough rests, heat oil in a low-sided six-quart saucepan over medium-high heat until a deep-frying thermometer registers 375°F.

Step 10

Flour your hands. Lift a fritter, pulling the ends to make a 4-inch oval; carefully drop into oil. Repeat with two more pieces of dough. Cook until fritters begin to brown, about 2 minutes. Using a slotted spoon, turn fritters over; cook until evenly browned, 2 minutes more. Transfer fritters to lined pan. Repeat with remaining dough.

Step 11

Coat fritters with white glaze. Transfer to a wire rack, and let glaze set. Serve warm or at room temperature.