01 - Preheat the oven to 350°F. Line two baking sheets with parchment paper and set aside.
02 - In a large mixing bowl, beat the softened butter and 1 cup of granulated sugar together using an electric mixer until the mixture is light and fluffy, approximately 2-3 minutes. Add the egg and vanilla extract, continuing to mix until fully incorporated.
03 - In a separate bowl, whisk together the all-purpose flour, baking powder, and salt. Gradually add the dry ingredient mixture to the wet ingredients, mixing on low speed until just combined. Cover the dough and refrigerate for 20 minutes to firm up.
04 - While the dough chills, combine the softened cream cheese, 1/3 cup granulated sugar, and 1 teaspoon vanilla extract in a small bowl. Beat until the mixture is smooth, creamy, and free of lumps.
05 - Roll tablespoon-sized portions of the chilled dough into balls and place them on the prepared baking sheets, spacing approximately 2 inches apart. Press your thumb into the center of each dough ball to create a deep well. Fill each indentation with about 1 teaspoon of the cheesecake mixture.
06 - Bake for 11-13 minutes, or until the cookie edges are lightly golden and the cheesecake filling appears set. Allow the cookies to rest on the baking sheets for 5 minutes before transferring to a wire cooling rack.
07 - In a microwave-safe bowl, combine the caramel candies with 1 tablespoon of heavy cream. Microwave in 30-second intervals, stirring between each burst, until the caramel is completely melted and smooth.
08 - Drizzle the warm caramel sauce generously over each cooled cookie. Allow the caramel to set at room temperature before serving. Optionally, sprinkle with flaky sea salt for a sweet-and-salty finish.