Mix flour, sugar, salt, yeast, nutmeg, cinnamon, baking soda, and cloves in a food processor or stand mixer.
Add apple cider, rose water, and almond extract (if using); mix until a sticky dough forms.
Add hazelnut oil or brown butter; mix just until combined.
Transfer dough to a greased bowl, cover, and let rise until doubled (about 2 hours).
Roll dough on a floured surface to about 1/2 inch thick.
Cut into 3-inch rounds, then cut out 1-inch centers to make rings.
Place on a greased baking sheet, cover, and let rise until puffy (about 1 hour).
Heat 3 inches of coconut oil in a Dutch oven to 365°F (185°C).
Fry donuts in batches, turning, until golden (about 75 seconds per side).
Drain on paper towels.
Mix sugar, cinnamon, and apple pie spice in a wide dish.
While warm, coat donuts in the sugar mixture.
Serve fresh and warm, or store in an airtight container for up to 2 days.