Whip the cream cheese. In a large bowl, add the cream cheese and beat on high speed until fluffy. You can use a stand mixer or a handheld mixer for this.
Add powdered sugar. Add the powdered sugar and mix on low speed until combined. Increase the speed to high and beat for an additional 30 seconds.
Add strawberries. Fold the chopped fresh strawberries into the mixture.
Freeze. Divide the mixture into 12 scoops (about 1 tablespoon each) and place them on a cookie sheet lined with parchment paper. Place in the freezer for at least 3 hours or until firm. (I prefer freezing overnight.)
Make the Cookie Dough
Cream the butter and sugar. In a large bowl, beat the butter, granulated sugar, and light brown sugar on high speed for 2 minutes. You can use a stand mixer or a handheld mixer for this.
Add the egg and vanilla. Add the whole egg and mix until combined, then add the egg yolk and mix until smooth. Add the vanilla extract and mix until smooth.
Add the dry ingredients. Add the all-purpose flour, baking powder, baking soda, and salt and mix on low speed until combined and smooth.
Fold in the strawberries. Add the strawberries and mix just until they have incorporated evenly into the dough. Be careful not to overmix as this will cause the strawberries to release their juices.
Chill the cookie dough. Cover the mixing bowl and chill in the refrigerator for at least 1 hour.
Assemble the Stuffed Cookies and Bake
Prep. Preheat the oven to 350ºF and line a baking sheet with parchment paper.
Remove the dough and filling. Once the cheesecake filling and cookie dough have chilled for their allotted time, remove them from the fridge and freezer.
Portion out the dough. Use a cookie scoop to measure out 12 balls of cookie dough. Place the balls on the prepared cookie sheet.
Fill the cookies. Use the back of a spoon to make a large indentation in each dough ball. Place a frozen ball of cheesecake filling in the indentation of each cookie. Gently close the dough around the cheesecake filling. Once the filling is enclosed, gently roll the dough into a ball.
Prepare the pan. Place the stuffed cookie dough balls on the baking sheet. You can bake 6 cookies on a standard-size baking sheet, so you may need to bake in batches. If you do, keep the extra dough and cheesecake filling cold between batches.
Bake. Bake in the preheated oven for 20-22 minutes or until the cookies are light golden brown and just set.
Cool completely. Remove the cookies from the oven and allow them to cool for 10 minutes in the pan before transferring them to a wire rack to cool completely.