Whisk the dry ingredients. In a medium bowl, whisk together the flour, baking soda, baking powder, and salt.
Set aside.
Cream the butter and sugars. In a large bowl, beat the softened butter with the granulated and brown sugars until light and fluffy, about 2–3 minutes.
Add the egg and flavorings. Beat in the egg, sour cream (or yogurt), lime zest, lime juice, and vanilla until smooth.
The mixture may look slightly curdled from the citrus—that’s okay.
Combine wet and dry. Add the dry ingredients to the wet and mix on low just until combined. Do not overmix.
The dough will be soft and slightly sticky.
Chill the dough. Cover and chill for 20–30 minutes. This helps the cookies bake thicker and stay soft.
Prep the oven. Heat to 350°F (175°C).
Line two baking sheets with parchment paper.
Scoop and shape. Use a medium cookie scoop (about 1.5 tablespoons) to portion the dough onto the prepared sheets, spacing 2 inches apart.
Bake. Bake for 9–11 minutes, until the edges are set and the tops look just dry.
The centers should still feel soft. Do not overbake—they’ll firm up as they cool.
Cool. Let the cookies rest on the sheet for 5 minutes, then transfer to a rack to cool completely.
Make the glaze. In a small bowl, whisk the powdered sugar with 2 tablespoons lime juice and a pinch of salt until smooth.
Add the remaining juice only if needed for a drizzleable consistency.
Glaze and finish. Spoon or drizzle the glaze over the cooled cookies. Sprinkle with extra zest if you like.
Let the glaze set for 20–30 minutes before serving.