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 on medium speed until pale, light, and fluffy, about 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 mixture to the wet ingredients, mixing on low speed until a soft dough forms. Cover and refrigerate the dough for 20 minutes to firm up for easier handling.
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 silky smooth and free of lumps.
05 - Roll tablespoon-sized portions of chilled dough into balls and arrange them on the prepared baking sheets, spacing about 2 inches apart. Press a deep indentation into the center of each ball using your thumb or the back of a teaspoon. Spoon approximately 1 teaspoon of the cheesecake filling into each well.
06 - Bake at 350°F for 11 to 13 minutes, until the cookie edges are lightly golden and the centers appear set. Allow cookies to rest on the baking sheets for 5 minutes before transferring to a wire cooling rack.
07 - Place the 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.
08 - Drizzle the warm caramel sauce generously over each cooled cookie. Allow the caramel to set at room temperature before serving. Optionally, finish with a light sprinkling of flaky sea salt.