Begin by creaming together the softened butter and sugar in a large mixing bowl using an electric mixer, blend on medium speed for about 2-3 minutes until light and fluffy.

Add the baking soda, cream of tartar, and salt to the butter-sugar mixture and mix on low speed until well combined.

Add the egg and vanilla extract to the dough and blend on medium speed until fully integrated.

Zest one lime and juice it, then mix both the zest and juice into the cookie dough until evenly distributed.

Gradually add the flour to the mixture while stirring on low speed until just combined.

Cover the bowl and refrigerate the dough for about 2 hours.

Preheat your oven to 375°F (190°C). Scoop tablespoon-sized portions of dough, roll them into balls, and coat in sugar. Place them on a lined baking sheet.

Bake for 8-10 minutes, until the edges are set but the centers remain slightly soft.

While the cookies are baking, prepare the glaze by melting butter, whisking in lime juice and powdered sugar.

Once cookies cool slightly, drizzle the glaze over them before transferring to a wire rack.