In a medium bowl, combine cream cheese and icing sugar. Cream with an electric mixer on medium speed until smooth.
Line a large baking sheet with parchment paper. Scoop small balls of cream cheese mixture (approximately 2 Tbsp) onto the baking sheet. Move the cheesecake batter to the freezer for 1 hour.
In a large bowl, combine the butter, granulated sugar and brown sugar. Beat with an electric mixer until smooth. Add eggs and vanilla extract. Beat with an electric mixer until smooth.
Add baking soda, flour, and salt. Beat until just combined.
Add toffee bits and chocolate chips. Fold into the cookie batter with a rubber spatula.
Remove cream cheese balls from the freezer. Transfer the parchment paper and balls onto a clean work surface. Line the baking sheet with a new piece of parchment paper.
Scoop approximately 2 tablespoons of cookie batter and form a small disc.
Place a frozen cream cheese ball in the center.
Scoop an additional tablespoon of cookie dough and cover the cream cheese ball completely, pressing the outer rim of the cookie dough together.
Place stuffed cookie dough onto the prepared baking sheet. Repeat this step until all of the remaining cookie dough has been used.
Add extra toffee bits and mini chocolate chips to the top of stuffed cookie dough discs. Freeze the stuffed cookie dough for 1 hour.
Preheat the oven to 350°F. Leave 6 stuffed cookie dough discs on the prepared baking sheet, transfer the other 6 back to the freezer. Bake for 14-16 minutes or until the edges are golden brown. Wait 5-10 minutes before transferring cookies to a cooling rack. Repeat step with remaining stuffed cookie dough discs. Allow cookies to cool completely before eating. Enjoy!