1. Sift flour, baking powder and salt into medium bowl and mix well. Whisk eggs in a large bowl until blended. Add sugar, oil, vanilla extract, and lemon zest and mix well. Stir the dry ingredients into egg mixture until blended chill, covered, for 30 minutes or longer.
2. Preheat the oven to 400°F. Drop the cookie dough by rounded teaspoonfuls 2 inches apart onto ungreased baking sheets. Mist the bottom of a 3-inch flat-bottom glass with water and dip glass in additional sugar. Press the top of each cookie lightly with the glass to flatten, misting glass with water and dipping in sugar before pressing each cookie.
3. Bake cookies until lightly browned about 8 minutes. Cool on baking sheets for 2 minutes. Remove to wire racks to cool completely. Store in airtight containers or freeze for future use.