Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper and set aside.
Make the cheesecake filling: in a bowl, beat 4 ounces softened cream cheese with 0.25 cup powdered sugar and 0.5 teaspoon vanilla until smooth. Set aside.
In a large bowl, cream together 0.5 cup softened unsalted butter, 0.75 cup granulated sugar, and 0.5 cup packed brown sugar until light and fluffy, about 2 to 3 minutes.
Add 1.0 large egg and 1.0 teaspoon vanilla extract to the butter mixture and beat until combined.
Whisk together 2.0 cups all-purpose flour, 1.0 teaspoon baking powder, and 0.5 teaspoon salt in a separate bowl, then gradually add to the wet ingredients and mix until just combined.
Fold 1.5 cups semi-sweet chocolate chips into the dough.
Portion the cookie dough into 24 equal balls (about 1.5 tablespoons each). Flatten each dough ball slightly, place a teaspoon of the cheesecake filling in the center, then top with another small piece of dough and seal edges to enclose the filling.
Place assembled cookies 2 inches apart on the prepared baking sheets. Bake in preheated oven for 10 to 12 minutes, until edges are lightly golden and centers are set.
Allow cookies to cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.
Store cooled cookies in an airtight container in the refrigerator for up to 5 days or freeze for longer storage.
Notes
For a firmer cheesecake center, chill the filling for 30 minutes before assembling. Cookies keep best refrigerated due to the cream cheese filling.