Heat oven to 350℉/177℃.
Line sheet pan with parchment paper. Set aside.
In a medium bowl, whisk flour, graham cracker crumbs, salt, baking soda, and cornstarch together. Set aside.
Combine butter, granulated sugar, and brown sugar in a medium bowl.
Beat with an electric mixer until well combined and creamy, about 1-2 minutes.
Add egg, egg yolk, and vanilla.
Beat until light and fluffy, about 2-3 minutes.
Mix in flour mixture.
Use a 3 Tablespoon cookie scoop to portion dough onto prepared pan.
Push a plug of frozen cheesecake mixture into the top of each cookie.
Bake for 12 minutes, or until golden brown.