Special equipment: A 3-inch doughnut cutter; a frying thermometer
For the ground pistachios: Pulse the pistachios in a food processor until it becomes coarse crumbs with some large chunks (do not grind to a butter). Separate out 50 grams ground pistachios for the phyllo crackers.
For the cake doughnuts: Combine the flour, baking soda, salt, cinnamon, nutmeg and orange zest in a medium bowl. Set aside.
Combine the milk and vinegar in a small bowl (it will curdle). Set aside.
Beat together the butter and sugar with an electric mixer on high, 3 minutes. With the mixer running, add the eggs one at a time and continue to beat, 3 minutes more. Turn off the mixer and add the sour cream and vanilla to the egg mixture. Mix on low until just incorporated.
Add the flour mixture and the milk mixture to the butter mixture in 3 stages, beginning and ending with the flour mixture and alternating in between them. Mix until just incorporated. Cover and chill, 10 minutes.
On a lightly floured surface, roll the dough out to a 1 1/2-centimeter thickness. Cut out doughnuts, using a 3-inch cutter. (The scraps can be re-rolled.)
In a large Dutch oven, bring 4 to 5 inches oil to between 350 and 360 degrees F. Fry the doughnuts, several at a time, flipping the doughnuts once a minute, until a skewer inserted into the center of the doughnut comes out clean (remove the doughnut from the oil before testing), 5 to 6 minutes total. Transfer to a wire rack to cool.
For the orange blossom syrup: Combine the sugar with 100 milliliters water in a small pot and bring to a boil. Add the orange blossom water and let simmer, 3 minutes. Remove from heat and cool.
For the phyllo crackers: Preheat the oven to 350 degrees F and brush a sheet pan with some clarified butter. Lay a sheet of phyllo on the sheet pan, then brush with the butter, sprinkle with half of the reserved 50 grams ground pistachios and drizzle with half the honey. Add another layer of phyllo and repeat brushing with butter, sprinkling with the remaining half pistachios and drizzling with the remaining half honey. Layer on the remaining sheet phyllo and brush with the butter. Cut the dough into small triangles, but leave them in place on the sheet pan. Bake until golden brown, 7 to 10 minutes. Let cool.
Set up a bowl with orange blossom syrup and another with the remaining 300 grams ground pistachios. Place a wire rack over a sheet pan.
Soak each doughnut in the orange blossom syrup for 30 seconds, then remove and let the excess syrup drip back into the bowl, 30 seconds. Dunk the doughnuts in the ground pistachios and transfer to the wire rack to set. Top each doughnut with 1 or 2 phyllo crackers and serve while warm.
This recipe was created by a contestant during a cooking competition. It has not been tested for home use.