For the doughnuts: In a mixing bowl, add the yeast to 1 cup warm water, mix with a fork and let sit for 5 minutes. Add the flour, milk, sugar, olive oil, zest and salt. Mix thoroughly until the batter is smooth, 2 minutes. Cover the bowl with plastic wrap and rest the dough in a warm place for 1 hour.
Preheat the deep fryer to 375 degrees F.
Dip a tablespoon measure in water, and then scoop out 1 tablespoon of dough. Wet your hands and roll the dough into balls, about 16 total. Place the doughnuts, a few at a time, in the fryer and cook until golden, 2 to 3 minutes.
For the honey: Place the honey, walnuts and 1/4 cup water in a pot set over medium heat for 3 minutes.
Coat the doughnuts with the walnut honey to serve.