In a shallow bowl, add ¼ cup of granulated sugar and mix in the ½ teaspoon of fresh lime zest into the sugar; set aside.
In a large bowl, whisk together the flour, baking powder, salt, and remaining 1 teaspoon zest. Set aside.
In a stand mixer with the paddle attachment, cream together the butter and remaining 1 cup of sugar for about 3 to 4 minutes, until light yellow and fluffy, scraping down the sides with a spatula as necessary.
Add the egg, egg yolk, vanilla, and key lime juice. Mix on low until the ingredients are well incorporated.
Gradually add in the dry ingredients (the flour mixture) until the batter is creamy and consistent.
Transfer dough to a bowl and cover with plastic wrap, or form dough into a log and wrap in parchment paper. Chill dough in the refrigerator for at least 30 minutes up to 2 hours.
Before taking the dough out of the refrigerator, preheat your oven to 350°F. Line two baking sheets with parchment paper.
Take the dough out of the refrigerator and use a scoop or a spoon to scoop out approximately one heaping tablespoon full of dough to form a ball. Roll dough ball into the prepared shallow bowl that has the ¼ cup granulated sugar with ½ teaspoon lime zest, until coated on all sides. Place onto the prepared lined baking sheet. Repeat with the remaining dough, placing dough balls approximately 2 inches apart since the dough will spread.
Bake at 350°F for 10 to 12 minutes, just until the centers are no longer glossy. If baking two pans at a time, be sure to rotate the pans from one rack to the other, and from back to front, halfway through the baking time.
Allow cookies to cool on the pan for 5 minutes before transferring to a cooling rack.
Notes
Makes approximately 30 cookiesKey limes: Key limes are smaller than regular limes and have a distinctive, stronger aroma and flavor. If you cannot find key limes, you may use regular limes. Storage: Store cookies in an airtight container for up to 5 days. To freeze the dough before baking: simply follow through Step 6 above, and place the dough log into a freezer-safe resealable plastic bag, seal tightly, for up to one month. Allow the frozen dough to thaw slightly at room temperature (about 15-30 minutes) before baking. To freeze baked cookies: allow the cookies to cool completely. Then store in an airtight, freezer-friendly container with parchment paper between each row of cookies to prevent them from sticking to one another. Seal shut, and freeze for up to one month. Allow to thaw before eating.