Step 1

Place a rack in middle of oven; preheat to 350°. Whisk 1½ cups plus 1 Tbsp. (200 g) all-purpose flour, ¼ cup (32 g) cornstarch, and ¾ tsp. Diamond Crystal or ½ tsp. Morton kosher salt in a medium bowl to combine. Using an electric mixer on medium speed, beat ½ cup (1 stick) unsalted butter, room temperature, 4 oz. cream cheese, room temperature, ¾ cup (83 g) powdered sugar, and 2 tsp. finely grated lime zest in a large bowl until combined. Increase speed to high and continue to beat, scraping down sides of bowl with a rubber spatula as needed, until smooth and slightly fluffy, about 1 minute. Add 2 Tbsp. fresh lime juice and 2 tsp. vanilla extract and beat on medium speed just until combined. Reduce speed to low, add dry ingredients, and mix again to combine. Using a rubber spatula, fold dough several times, scraping bottom and sides, to make sure it’s thoroughly mixed.

Step 2

Fit a pastry bag or resealable plastic bag with a ½" star tip and transfer dough to bag, doing your best not to create any air pockets. Push dough to bottom of bag, pressing out any air, and twist bag to seal. Applying constant, even pressure, pipe dough onto a large parchment-lined baking sheet in tight squiggle shapes about 3" long, spacing about 1" apart (they won’t spread much). Chill, uncovered, until dough is firm, 15–20 minutes. (If it’s cold in your kitchen, the butter in the dough could firm up and make it difficult to pipe. If this happens, place the bag in a warm spot and let sit until softened.)

Step 3

Bake cookies until ridges are golden and sides are firm, 18–22 minutes. Let cool on baking sheet.

Step 4

Whisk 1 cup (110 g) powdered sugar, 2 Tbsp. fresh lime juice, and 1 Tbsp. unsalted butter, melted, slightly cooled, in a medium bowl until smooth. Holding a cookie around its sides, dip upside down into glaze so everything except bottom is submerged. Wiggle gently for a few seconds to encourage ridged surfaces to pick up glaze. Lift up cookie and let any excess glaze drip back into bowl. Place glaze side up on a wire rack. Using a Microplane, grate some lime zest over cookie while glaze is still wet. Repeat with remaining cookies. Let sit until glaze is set, 25–30 minutes.Do ahead: Cookies can be made 3 days ahead. Once glaze is set, stack in an airtight container, separating layers with sheets of parchment paper. Store at room temperature. Piped, unbaked cookies can be made 2 months ahead. Freeze solid on baking sheet, then transfer to a resealable plastic freezer bag. Bake as directed (no need to thaw first).