In a medium bowl, dissolve yeast with the warm water and sugar. Stir in 1 cup the flour. Cover the bowl with plastic wrap and let sit for about 1 hour.
In a separate bowl, sift together the remaining flour with salt, cinnamon and nutmeg.
Using a paddle attachment beat the butter until fluffy in a standing mixture for about 30 seconds. Add sugar and beat for another minute. Add eggs, one at time, until blended.
Add yeast mixture along and flour mixture and mix medium speed for 2 – 3 min. Transfer the dough to a buttered bowl. Cover and leave at room temperature for 1 hour before rolling into doughnut holes, approximately 1-inch in diameter.
Pour pure olive oil in a heavy pot and heat to 350°F.
Drop the doughnuts holes into the oil (six at a time). Fry until puffed and golden all over, turning once. Remove the doughnut holes as they’re done and let cool on a cooling rack for approx. 5 min. Place cooled doughnut holes in a medium sized bowl. Toss and coat in sugar mixture. Share.