Mix whole wheat flour, baking powder, cinnamon, salt, nutmeg, and sugar in a large bowl. Stir eggs, vanilla, milk, and ¼ cup evoo in a separate bowl.
Add wet ingredients to dry ingredients and mix. Knead dough for a few minutes.
Take about 2 tablespoons of the dough and roll into a small ball, flatten in your hand, and spoon in a drop of jelly. Fold up the dough to cover the jelly, maintaining the round shape.
Heat ¼ cup evoo in a frying pan over high heat. Once hot, add doughnut and roll it around in the oil until all sides are golden-brown. Watch closely to prevent overcooking.
Remove from heat and allow to drain on paper towels.
Before serving, heat in hot oven for 5 minutes.