Combine flour, baking powder, baking soda and salt in a medium bowl. Whisk together, set aside.
With an electric-mixer on medium speed, beat butter and sugar until creamy. Beat in egg and vanilla until light and fluffy.
Gradually add in flour mixture until a soft dough forms. Divide the dough in half. Flatten each half into a 4-inch disc. Cover with plastic wrap and refrigerate atleast 30 minutes or overnight.
Preheat oven to 350° F. Line two large baking sheets with parchment paper. Sprinkle dough lightly with flour. Roll one disc of dough out on a lightly floured countertop. Roll dough to 1/2 inch thickness. With a 3-4 inch egg shaped cookie cutter, cut dough out. Transfer egg shapes to baking sheets. Repeat with remaining dough.
Bake cookies until lightly browned around edges, about 10 minutes. Let cook completely before icing.