In a small saucepan, simmer 1 cup of apple cider over medium heat until it has reduced to about 1/4 cup. This should take 10-15 minutes. Set it aside to cool; this concentrated syrup will be the base for your glaze.
In a medium saucepan, combine the water, butter, sugar, and salt. Bring the mixture to a rolling boil over medium-high heat. Once boiling, add the flour all at once. Stir vigorously with a wooden spoon until the mixture forms a ball and pulls away from the sides of the pan. Continue to cook and stir for another 1-2 minutes to cook off excess moisture.
Transfer the dough to a large bowl and let it cool for 5 minutes. Using a hand mixer or a wooden spoon, add the eggs one at a time, beating thoroughly after each addition. The dough will look like it is breaking at first, but keep mixing until it becomes smooth and glossy. Stir in the vanilla extract.
Fit a piping bag with a large open star tip (like a Wilton 1M or 2D). Pipe 3-inch circles onto small squares of parchment paper. The parchment paper will help you drop the donuts into the oil without ruining their shape.
Heat 2-3 inches of oil in a heavy pot to 350°F (175°C). Carefully pick up a parchment square and place it dough-side down into the oil. After about 30 seconds, the paper will release; remove it with tongs. Fry the donuts for 2-3 minutes per side until they are deep golden brown and puffed. Drain on a wire rack.
In a medium bowl, whisk together the reduced apple cider, powdered sugar, cinnamon, and nutmeg until smooth. If the glaze is too thick, add a teaspoon of water or cider. If it is too thin, add a bit more powdered sugar.
While the donuts are still slightly warm, dip the top half of each cruller into the apple cider glaze. Place them back on the wire rack to let the glaze set for a few minutes before serving.