Combine the eggs, sugar, vanilla and yogurt in a bowl. Slowly whisk in enough of the flour to form a thick batter. Allow batter to rest about 10 minutes.
Place oil in a 1 1/2-quart saucepan (you want about 2 inches of oil in the pan) and heat to 325F. With a teaspoon, drop small mounds of batter into the hot oil and cook 3 to 4 minutes, turning the sufganiyot with the spoon or a slotted spatula, until golden brown and cooked through. Drain on a plate lined with paper towel.
While still warm, place on a platter and sprinkle with powdered sugar.
