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 pale, light, and fluffy. Add the egg and vanilla extract, then 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 just combined. Do not overmix. Cover and chill the dough 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 until smooth, creamy, and free of lumps.
05 - Roll tablespoon-sized portions of chilled dough into balls and place on the prepared baking sheets, spacing them about 2 inches apart. Press your thumb into the center of each ball to form a deep well. Spoon approximately 1 teaspoon of the cheesecake filling into each well.
06 - Bake for 11 to 13 minutes, or until the cookie edges are set and lightly golden. Allow the cookies to rest on the baking sheets for 5 minutes, then transfer to a wire rack to cool completely.
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 before serving. Sprinkle with flaky sea salt for added flavor if desired.