Position a rack in the middle of the oven. Preheat the oven to 325 degrees F. Line one baking sheet if making 9 cookies, or two baking sheets if making 13 cookies, with parchment paper.

Make the Cookies
Sift the flour, cornstarch, baking powder, and salt into a medium bowl and set aside. In a large bowl, using an electric mixer on medium speed, beat the butter, powdered sugar, and vanilla until smooth and creamy, about a minute. Stop the mixer and scrape the sides of the bowl as needed during mixing. On low speed, add the flour mixture, mixing until it is incorporated and the dough holds together in large clumps and comes away from the sides of the bowl.

Form the dough into a smooth ball. Lightly flour the rolling surface and rolling pin. Roll the dough out to a 1/4-inch thickness. Using a 4 1/2 or 3 1/2-inch-long heart-shaped cutter, cut out the hearts. Use a thin metal spatula to transfer them to the prepared baking sheets, placing them about 1 inch apart. Gather together the dough scraps, roll them, and cut out additional hearts.

Bake one sheet at a time until the edges and bottoms of the cookies are lightly browned, about 20 minutes. Cool the cookies on the baking sheet for 5 minutes, then use a wide metal spatula to transfer them to a wire rack to cool completely.

Make the Glaze
In a small bowl, stir the powdered sugar and vanilla together with enough cream to form a thick, spreadable glaze. Use a thin metal spatula to spread half of each cookie heart with glaze. Let the cookies sit until the glaze is firm.

The cookies can be layered between sheets of wax paper in a tightly covered container and stored at room temperature for up to 4 days.