In a large measuring jug, add 255 grams (1 cup plus 2 tablespoons) apple cider, rose water and almond extract, and stir to combine. Set aside.
In your food processor, add the flour, sugar, salt, yeast, nutmeg, cinnamon, baking soda and cloves, and pulse a few times to combine.
With the processor running, add the apple cider mixture. Let the machine run for about 50 seconds, until a soft, sticky dough is formed.
With the processor still running, add the browned butter or oil, and process for another 10 seconds.
Transfer the dough to a lightly greased mixing bowl.
Cover and let rest, until dough is puffy and doubled in size, about 1 hour.
Transfer the dough to a lightly dusted surface.
Using a rolling pin, roll out the dough to about ½ inch thickness.
Dust off any excess flour, and cut into 3-inch rounds.
If not using a doughnut cutter, poke a hole in the center of each round, and gently stretch the dough into a ring.
Arrange the doughnuts in a lightly greased tray.
Knead the scraps together, let rest for a few minutes, the repeat the rolling and cutting process.
Cover and let rise, until the dough has risen to almost ¾-inch thickness, 40 minutes.
Fry the doughnuts. In a large pot, add enough cooking oil up to 2 inches deep.
Heat the to 185 degrees C over medium heat.
Fry 4 to 5 doughnuts at a time, 1 minute 15 seconds per side.
If using an airfryer, spray the doughnuts with cooking spray, and fry at 180 degrees C in a single layer, 4 minutes.
Prepare the glaze. In a medium sized bowl, add the icing sugar and the remaining ¼ cup cider, and whisk until smooth.
When the doughnuts are cool enough to handle, dip into the cider glaze.
Transfer to a serving platter and serve immediately.