Preheat the oven to 400° F.
Sift the flour, baking powder, and salt into a bowl, mixing well.
In a large bowl, whisk the eggs.
Add sugar, vegetable oil, vanilla extract, and lemon zest. Mix together well.
Stir in the dry ingredients, mixing until well blended.
Cover the bowl with a clean towel and chill in the refrigerator for 30 to 60 minutes.
Drop 2″ balls of cookie dough onto an ungreased cookie sheet.
Dip the bottom of a dampened glass into the remaining sugar, and press down on the dough ball to flatten the cookie.
Dip a glass in sugar after flattening each cookie.
Bake for 8 to 9 minutes, until cookies are lightly browned.
Allow sugar drop cookies to cool completely. Then, store it in an airtight container.