Preheat the oven to 350ºF. Line 2 baking sheets with parchment paper and set aside. Whisk together the flour, salt, baking soda and baking powder. Set aside.
In the bowl of a stand mixer, cream together the butter and sugars until light and fluffy, about 5 minutes, scraping down the sides of the bowl as needed. Add in the egg until fully incorporated. Next, add the tequila and lime zest, mixing on medium-low speed. The dough may look curdled, but will come together as you keep mixing. Once fully mixed, turn the mixer off and add the dry ingredients. Mix on low speed until just incorporated. Stop while there are a few flour streaks remaining and finish mixing by hand.
Using a medium cookie scoop, about 1½ tablespoons, scoop out the dough onto the prepared baking sheets. Leave about 1-inch between the cookies. At this point you can bake the cookies right away or cover with plastic wrap and refrigerate up to 12 hours.
Bake the cookies one pan at a time in the center of the oven for 13-15 minutes, until the edges are set and the center is still soft. Let cool on the pan for 5 minutes, then carefully transfer to a wire rack to cool fully.
In the meantime, make the glaze: mix together the powdered sugar and tequila in a bowl until smooth. Drizzle over the cooled cookies. Top with lime zest.
Store cookies in an airtight container at room temperature up to 5 days.
Recipe by Lenses and Lentils at https://lensesandlentils.com/glazed-margarita-cookies/