Step 1: Prepare the Cheesecake Filling: In a medium bowl, beat the softened cream cheese with granulated sugar, vanilla extract, and egg yolk until smooth. Stir in the 2 tablespoons of all-purpose flour until just combined. Drop by teaspoonfuls onto a parchment-lined plate (about 18-24 balls). Freeze for at least 30-60 minutes, or until firm.
Step 2: Prepare the Cookie Dough: In a large bowl, cream together the softened butter, granulated sugar, and brown sugar with an electric mixer until light and fluffy. Beat in the egg and vanilla extract until well combined.
Step 3: Combine Dry Ingredients: In a separate bowl, whisk together the 1 3/4 cups all-purpose flour, baking soda, and salt. Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Stir in the chocolate chips.
Step 4: Chill the Cookie Dough: Cover the cookie dough and refrigerate for at least 30 minutes. This helps prevent spreading.
Step 5: Preheat Oven & Prepare Baking Sheets: Preheat your oven to 375°F (190°C). Line two baking sheets with parchment paper.
Step 6: Assemble the Cookies: Take about 1.5 tablespoons of cookie dough and flatten it into a disk. Place one frozen cheesecake ball in the center. Carefully wrap the cookie dough around the cheesecake ball, sealing completely to enclose the filling. Roll into a smooth ball.
Step 7: Bake the Cookies: Place the stuffed cookie dough balls about 2 inches apart on the prepared baking sheets. Bake for 12-15 minutes, or until the edges are golden brown and the centers are set. The cheesecake might peek out slightly, which is normal.
Step 8: Cool and Serve: Let the cookies cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely. Enjoy warm for the best gooey center!