Make cheesecake filling: In a small mixing bowl, combine 8 ounces cream cheese, ¼ cup sugar, and 1 teaspoon vanilla. Using a hand mixer, mix for about 2 minutes or until it's light and fluffy.
Freeze cheesecake filling: Using a small cookie scoop (about 1 to 1 ½ tablespoons), scoop the filling into 12 balls on a parchment paper lined cookie sheet. Gently press down on each ball to flatten the cheesecake scoop. Place the cheesecake discs in the freezer for about 20 minutes.
Prepare and preheat: Meanwhile, preheat the oven to 350°F. Line two baking sheets with parchment paper.
Cream wet ingredients: In a large bowl, using a mixer, cream together the 1 cup butter, 1 cup sugar, and 1 cup brown sugar for about 1 minute. Add the 2 eggs and 1 tablespoon vanilla and beat just until combined.
Add dry ingredients: Add the 3 cups flour, 1 teaspoon baking soda, ¾ teaspoon salt, and 1 teaspoon cornstarch to the wet mixture and mix on low speed until just combined.
Form cookies around cream cheese: Using a medium cookie scoop (about 2 tablespoons), scoop the cookie dough into 24 balls on the prepared baking sheet. Slightly flatten each and lay a cheesecake disc on 12 of the balls. Place another cookie dough ball on top, and mold around the cheesecake so it's covered completely. Chill in the fridge for 30 minutes to set the shape.
Bake and cool: Put 6 cookies on each cookie sheet and bake for 10 to 12 minutes. Allow cookies to set on the pan for 10 minutes before transferring them to a cooling rack.