Prepare the dough: In the bowl of a stand mixer with the paddle attachment, add the cider, water, yeast, sugar and melted butter and combine. Add 2 cups of flour. Once incorporated, add the salt and the rest of the flour. Mix the dough together for 5 minutes on medium speed.
Cover the bowl with a clean kitchen towel and allow to rise until doubled, about 2 hours.
Prepare the apples: In a large skillet, combine the apple cider, lemon juice, cinnamon, nutmeg, vanilla bean and butter. Bring the mixture to a simmer over medium low heat and reduce the liquid by half until slightly thickened and syrupy.
Add half of the apples and cook until just softened, about 5 minutes. Transfer this mixture to a large bowl to cool, then add the remaining diced apples. Set aside until cooled to room temperature.
Assemble the donuts: Add the oil to a large Dutch oven and set it on the stove over high heat.
While the oil climbs to 350°F, roll out the dough on a lightly floured surface until it’s roughly 8 x 11 inches.
Add 1/3 of the cooled apples to the right side of the dough, then fold the left side over the apples. Give the dough a turn so the opening is now at the bottom.
Roll out the dough again and repeat the process until all the apples have been used. This is a messy process and will require some pesky runaway apples to be tucked back into the dough. If at any point the dough seems reluctant to roll out, simply give it a 5 minute rest then return to a much more relaxed and manageable dough.
Once all the apples have been folded into the dough, roll it out one final time into a rectangle that is about 1/2-inch thick. Cut the fritters into rough 1 1/2 inch squares.
Let them rest for a few moments before frying them in small batches.
Take care to keep the oil at a consistent 350°F. Fry the fritter until deeply golden and cooked through, about 5 minutes, flipping them once, halfway through.
Remove the fritters — and any apples that have fallen out — with a slotted spoon or a Chinese spider. Let them cool briefly on a wire rack.
Continue frying in this way until all the fritters have been fried.
Prepare the glaze: In a medium bowl, whisk together the powdered sugar, heavy cream, apple cider, lemon juice, and salt.
Drizzle the glaze over the fritters while they are still warm. Finish with flake salt if desired.