Preheat oven to 350˚F (180˚C). Line two baking sheets with parchment or lightly grease.
In the bowl of a stand mixer fitted with the paddle attachment or a large bowl, beat together the eggs and sugar until light and pale. Slowly beat in olive oil, lemon zest, and vanilla extract.
In another bowl, whisk together the flour, baking powder, and salt. Mix into the egg mixture until just combined.
Scoop out a tablespoon-sized ball of dough (0.7 ounces/20 grams). Using lightly wet hands, roll the dough into a ball and place on prepared baking sheet. Repeat with remaining dough, placing them two inches (5 centimeters) apart.
Wet the circular handle of a wooden spoon and use it to poke a hole in the center of the ball of dough, twisting to expand the size slightly to a little over 1/2 inch (1 1/2 centimeters). Wet the handle between balls of dough.
In a small bowl, beat the egg with the orange blossom water. Brush over the cookies and sprinkle with additional sugar.
Bake in preheated oven until golden, 15-18 minutes. Transfer the cookies to a wire rack and allow to cool. Repeat with remaining dough.
Store in airtight container for up to a week.