Make cheesecake filling: In a small mixing bowl, combine 8 ounces cream cheese, 1/4 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 (1 to 1 1/2 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 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, 3/4 teaspoon salt and 1 teaspoon cornstarch and mix on low. If the dough is too sticky add an extra Tablespoon or two of flour.
Form cookies around cream cheese: Using a medium cookie scoop (about 2 Tablespoons), scoop the cookie dough into 24 balls on the baking sheet. Slightly flatten each and lay a cheesecake disc on 12 balls. Place another cookie dough on top, and mold around the cheesecake so it's covered completely. Chill in fridge for 30 minutes.
Bake and cool: Put 6 cookies on each cookie sheet and bake for 10 - 12 minutes. Allow cookies to set on pan for 10 minutes before moving to colling rack.