Preheat the oven to 350°F (175°C). Line baking sheets with parchment paper and set aside.
In the bowl of a stand mixer fitted with the paddle (or using a hand mixer), beat the softened butter and granulated sugar on high speed for 3–5 minutes until light and fluffy, scraping down the bowl as needed.
Add the eggs, key lime zest, baking powder, vanilla extract, and salt; beat briefly to combine. Reserve the key lime juice for the glaze.
Scrape the bowl, then with the mixer on low speed slowly add the all-purpose flour until just incorporated. Do not overmix.
Use a 1½ teaspoon cookie scoop to portion small balls of dough. Roll between your hands if needed and place them 2 inches apart on the prepared baking sheets.
Bake for 10 minutes, until the cookies are domed and just beginning to turn golden at the edges. Remove from the oven and let cool on the pan for 5 minutes.
Meanwhile, make the glaze: in a medium bowl whisk together the powdered sugar, 2–3 tablespoons reserved key lime juice, and heavy cream until very smooth. Adjust juice or cream to reach a dip-able consistency.
Dip the top of each warm cookie into the glaze, then place the cookie dome-side up on a wire rack so the glaze can spread and set. If desired, sprinkle extra key lime zest over the wet glaze.
Allow glaze to set completely before stacking or storing the cookies.