Preheat your oven to 350°F and line two cookie sheets with parchment paper. Cream together the butter and sugars until they're light and fluffy, which should take about 3 to 4 minutes. Mix in the egg and vanilla.
In another bowl, whisk together the flour, cornstarch, baking soda, and salt. Then, add this mixture to the wet ingredients and mix until everything is smooth. The dough will be thick.
Use a small cookie scoop to place tablespoon-sized balls of dough onto the parchment-lined cookie sheets. Lightly press down on each cookie to flatten it slightly. Bake them until the edges start to brown, which usually takes about 9 to 10 minutes.
Once they're out of the oven, let the cookies cool for 2 to 3 minutes before transferring them to a cooling rack to cool completely.
To make the frosting, beat the cream cheese until it's smooth. Add the powdered sugar and vanilla, and mix until everything is smooth.
Put the granulated sugar into a small bowl. Spread about a tablespoon of frosting onto the tops of each cookie, then press them into the granulated sugar, coating the frosting with sugar.
Just before serving, use a kitchen torch to caramelize the sugar on top of each cookie. Then, set them aside to cool. You can store these cookies in the fridge for up to 4 days. Enjoy!