Cream the butter and sugars. In a large bowl, beat the softened butter, brown sugar, and granulated sugar until creamy and lighter in color. Scrape down the sides of the bowl.
Add the egg and vanilla. Beat in the egg and vanilla extract until fully combined.
Combine the dry ingredients. In a separate bowl, whisk together the flour, cornstarch, baking powder, and baking soda. Add to the butter mixture and mix on low speed just until the dough comes together.
Chill the dough. Cover and refrigerate for 20 minutes. Meanwhile, preheat the oven to 350°F (180°C) and line the baking sheets with parchment paper.
Shape the cookies. Divide the dough into 30 portions and roll into balls. Arrange on the prepared baking sheets, leaving about 2 inches between them. Keep any remaining dough refrigerated between batches.
Bake. Bake for approximately 12 minutes, until the edges are lightly golden and the tops are set. The centers should still feel slightly soft. Let rest on the baking sheet for about 5 minutes, then transfer to a wire rack to cool completely.
Make the glaze. Stir the sifted powdered sugar with 3 tablespoons (45 ml) milk until smooth. If necessary, add more milk, ½ teaspoon at a time, until the glaze flows slowly and coats a cookie without running off quickly.
Dip and decorate. Dip the top of each cooled cookie into the glaze. Let the excess drip back into the bowl, then turn icing-side up and place on a rack. Immediately add sprinkles, if using.
Let the icing set. Leave the cookies in a single layer until the glaze is dry before storing or stacking.