In a large mixing bowl, sift together the flour, baking soda, and salt. Whisk in the key lime zest.: Your nose will catch the first lift of citrus as you sift and whisk. The dry mixture should look uniform, with the flecks of key lime zest dispersed through the pale all purpose flour . This step matters because it distributes the leavening and zest evenly, preventing pockets of baking soda or intense citrus. If the zest clumps, break it apart with your fingers so each bite has brightness. A common mistake is skipping the sifting, which can lead to uneven rising and a denser cookie texture.
In the bowl of a stand mixer fitted with the paddle attachment, cream the butter, granulated sugar, and brown sugar until light and fluffy, about 2 minutes.: As you cream, you will notice the mixture lighten in color and grow slightly in volume, a sign the sugars are aerating the softened unsalted butter . This creates tiny air pockets that translate to a tender crumb. Listen for the quiet hum of the mixer and watch for a pale, creamy texture. If your butter is too cold the mixture will remain lumpy, so let it soften until it yields to gentle pressure. Overmixing can make the butter too soft; stop once it looks fluffy and holds soft peaks.
Add the egg, vanilla extract, and key lime juice to the butter mixture, mixing until fully incorporated.: When you add the egg , you will see the mixture become silkier and more cohesive. The aroma will shift as the vanilla extract and key lime juice meld with the butter, releasing a fragrant, slightly tangy scent. Mix just until incorporated to avoid overworking the batter, which can cause a tough result. If the mixture appears curdled after adding the egg, keep mixing briefly and it should come together; this is normal and not a cause for alarm.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Stir in the graham cracker crumbs.: As you fold the dry into the wet, the dough will thicken and pull away from the bowl sides. The gradual addition prevents lumps and helps maintain a tender texture. Once the dough forms, sprinkle in the graham cracker crumbs and fold until you see small, toasty flecks throughout. These crumbs add both flavor and structure. Avoid overmixing here, since excessive stirring develops gluten and can make the cookies tough; stop when you no longer see streaks of flour.
Scoop the cookie dough onto prepared baking sheets, spacing them a few inches apart. Bake at 350°F for 9 minutes or until the edges are just set. Let cool on the pan for 10 minutes before transferring to a wire rack.: As the cookies bake, watch for the edges to set and the centers to look slightly soft but not raw. The oven will coax out fragrant citrus and a faint caramel note from the sugars. The first minute after removing from the oven is noisy with residual bubbling, then the cookies settle; cooling on the pan allows carryover heat to finish them without overbaking. A common error is leaving them in too long which dries the centers, so take them out when the edges are firm and the centers still yield slightly to touch.
If desired, mix powdered sugar with a small amount of milk to create an icing; drizzle icing over cooled cookies.: The glossy drizzle offers a sweet counterpoint to the tart lime. The icing should be thin enough to drizzle but thick enough to set, so add milk sparingly until you reach a ribbon like consistency. Work on a wire rack with parchment underneath to catch drips. One misstep is icing warm cookies, which will cause the glaze to melt into the surface rather than form a pretty sheen; always ice after the cookies are fully cooled.