In a mixing bowl, cream the room-temperature salted butter, cornstarch, and 1/2 cup (57 g) confectioners' sugar with an electric mixer until smooth and well combined, about 3 minutes.
Add the all-purpose flour and mix just until incorporated and a soft dough forms.
Stir in 1 tablespoon lemon zest and 1 1/2 tablespoons lemon juice until evenly distributed.
Divide the dough in half and shape each half into a 1-inch diameter log on a sheet of parchment, wrapping and twisting the ends to seal.
Refrigerate the wrapped logs until firm, about 1 hour.
When ready to bake, preheat the oven to 350°F (175°C) and line a rimmed baking sheet with parchment paper.
Unwrap the chilled logs and slice into 1/4-inch thick rounds. Place slices on the prepared baking sheet about 1 inch apart.
Bake until set but not browned, about 10 minutes. Remove from the oven and let cookies cool completely on the baking sheet.
For the glaze, whisk together 1/2 cup (57 g) confectioners' sugar, 1 tablespoon lemon zest, and 2 tablespoons lemon juice until smooth.
Spoon about 1/2 teaspoon of glaze onto the center of each cooled cookie and spread lightly; allow the glaze to set before serving.