Preheat oven to 350°F (175°C) and line a baking sheet with parchment paper.

In a large bowl, cream together 1 cup softened butter and 1 cup granulated sugar until light and fluffy.

Beat in the eggs one at a time, then stir in 1 teaspoon vanilla extract.

Whisk together the flour, cornstarch, baking powder, and salt; gradually add to the wet ingredients until a soft dough forms.

In a small bowl, combine brown sugar, cinnamon, and melted butter to create the swirl mixture.

Divide the dough into 12 large balls and place on the baking sheet.

Make an indentation in each ball, place a spoonful of the cinnamon mixture inside, and lightly swirl with a toothpick.

Bake for 10-12 minutes or until the edges are just set; do not overbake.

Allow cookies to cool completely on the pan.

For the frosting, beat cream cheese and 1/4 cup butter until smooth, then add powdered sugar and 1/2 teaspoon vanilla extract.

Pipe a spiral of frosting onto each cooled cookie and sprinkle with additional cinnamon if desired.