01 - Preheat 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 becomes light and fluffy, about 2-3 minutes. Add the egg and vanilla extract, then continue mixing 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 a soft dough forms. Cover and chill the dough in the refrigerator for 20 minutes.
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 with an electric mixer until completely smooth and creamy with no lumps remaining.
05 - Roll tablespoon-sized portions of the chilled dough into balls and place them on the prepared baking sheets, spacing about 2 inches apart. Press your thumb gently into the center of each dough ball to create a deep well.
06 - Spoon approximately 1 teaspoon of the cheesecake filling into the center well of each dough ball, filling evenly.
07 - Bake at 350°F for 11 to 13 minutes, until the cookie edges are set and lightly golden. Allow the cookies to rest on the baking sheets for 5 minutes before transferring to a wire cooling rack.
08 - Place the caramel candies and heavy cream in a microwave-safe bowl. Heat in 30-second intervals, stirring between each burst, until the caramel is completely melted and smooth.
09 - 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 added flavor contrast.