Preheat oven to 350°F (175°C) and line two baking sheets with parchment. Cream the softened butter and sugar with an electric mixer on medium speed until pale and fluffy, about 3 minutes.

Beat in the egg and vanilla extract on low speed just until smooth, about 30 seconds.

Whisk the flour, cornstarch, baking powder, and salt together, then gradually mix into the butter mixture on low speed until a soft dough forms, about 1 minute.

Lightly flour a surface and rolling pin, then roll the dough to 1/4 inch thickness. Cut into shapes and place on the prepared sheets, 1 inch apart.

Bake one sheet at a time for 10 to 12 minutes, just until the edges are set and tops are dry. Let the cookies rest on the sheet for 5 minutes, then transfer to a wire rack to cool completely.