01 - Preheat oven to 350°F. Line two baking sheets with parchment paper and set aside.
02 - In a large mixing bowl, beat softened butter and 1 cup granulated sugar with an electric mixer on medium speed until pale, light, and fluffy, about 2-3 minutes. Add the egg and vanilla extract; continue mixing until fully incorporated.
03 - In a separate bowl, whisk together all-purpose flour, baking powder, and salt. Gradually add the dry mixture to the wet ingredients, mixing on low speed just until the dough comes together. Do not overmix. Cover and refrigerate the dough for 20 minutes.
04 - While the dough chills, combine softened cream cheese, 1/3 cup granulated sugar, and vanilla extract in a small bowl. Beat with an electric mixer until completely smooth and creamy with no lumps remaining.
05 - Roll tablespoon-sized portions of chilled dough into balls and place on prepared baking sheets, spacing about 2 inches apart. Press your thumb or the back of a teaspoon into the center of each ball to create a deep well. Fill each indentation with approximately 1 teaspoon of the cheesecake mixture.
06 - Bake at 350°F for 11-13 minutes, until the cookie edges are set and lightly golden. The centers may appear slightly soft. Allow cookies to rest on the baking sheets for 5 minutes before transferring to a wire rack to cool completely.
07 - Place caramel candies and heavy cream in a microwave-safe bowl. Heat in 30-second intervals, stirring between each burst, until the mixture is completely smooth and pourable. Let cool slightly for 1-2 minutes.
08 - Drizzle the warm caramel sauce over each cooled cookie. Allow the caramel to set at room temperature for 15-20 minutes before serving.