Preheat oven to 350 degrees. Mix flour and baking powder and set aside.
With a mixer, cream together eggs and granulated sugar. Add oil, lemon zest, lemon juice and vanilla and combine. Add in flour mixture and mix together until smooth.
Using a cookie scoop or tablespoon, scoop out a ball of dough. Roll into a smooth rope and bend into a “U” shape. Twist the loose ends together two or three times and press ends together.
Bake for about 15 minutes, turning the cookie sheet half way through. Remove from oven and tray and cool.
For the glaze: Mix together 3 cups of powdered sugar and ⅓ cup lemon juice, thinning or thickening by adjusting the amount of juice or sugar. Dip or submerge the cookies in the glaze and place on a wire rack to dry.