Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper.
In a large bowl, cream together the softened butter, 1 cup granulated sugar, and brown sugar until light and fluffy.
Beat in the 2 large eggs one at a time, then stir in 1 teaspoon vanilla extract.
In a separate bowl, whisk together the flour, baking soda, and salt. Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Fold in the chocolate chips.
In a small bowl, beat the softened cream cheese with 1/4 cup granulated sugar, egg yolk, and 1/2 teaspoon vanilla extract until smooth.
Drop spoonfuls of brownie cookie dough onto the prepared baking sheets, leaving space between them.
Dollop small amounts of the cheesecake mixture on top of each brownie cookie dough mound. Use a knife or toothpick to swirl the cheesecake into the brownie dough for a marbled effect.
Bake for 10-12 minutes, or until the edges are golden and the centers are set.
Let the cookies cool on the baking sheets for a few minutes before transferring them to a wire rack to cool completely.
Notes
Ensure your butter and cream cheese are at room temperature for smooth mixing.
Do not overmix the cookie dough; this can make the cookies tough.
For best results, chill the dough for 30 minutes before baking to prevent spreading.