Preheat oven to 350° F. Put a sheet of parchment paper on a cookie sheet or sheet pan.
Use a hand mixer or stand mixer to beat together the butter and granulated sugar until combined. Make sure the butter has been softened to room temperature by letting it sit on the counter for at least 30 minutes (2 hours if the butter was in the freezer).
Add the vanilla extract, egg, and lemon and lime essential oils.* (You can substitute fresh or bottled lemon juice and lime juice.) Beat at medium speed until combined.
Add in the flour, baking powder, baking soda, and salt. If you are using a stand mixer, cover the bowl with a dishtowel to contain the dry ingredients until they are incorporated.
Put 3/4 cup powdered sugar in a small bowl.
Use a 1-inch cookie scoop to portion the dough. Roll the dough between your hands. Roll each ball of dough in the powdered sugar to fully coat it. Place onto the parchment-lined baking sheet, 2 inches apart. (If there is leftover powdered sugar, save it for the glaze.)
(If you are freezing the dough, put all the cookie dough balls onto one baking sheet, and place in the freezer for 10 minutes to set. Then transfer the cookie dough balls into a zippered freezer bag, squeezing out the air. Label the bag with the baking directions for future reference. Store in the freezer for up to 6 months.)
Bake for 10-11 minutes, until the bottoms are lightly golden brown. (If you are baking them right out of the freezer, bake for 12-13 minutes.) Let cool on the baking sheet for 2 minutes before transferring them to a cooling rack. Let cool completely before glazing.