01 - Preheat oven to 350°F. Line two baking sheets with parchment paper.
02 - In a large bowl, beat together the softened butter and 1 cup sugar using an electric mixer until light and fluffy, about 2-3 minutes. Add the egg and vanilla extract, mixing until fully incorporated.
03 - In a separate bowl, whisk together the flour, baking powder, and salt. Gradually add the dry mixture to the wet ingredients, mixing on low speed until just combined. Chill the dough for 20 minutes.
04 - While the dough chills, beat the cream cheese, 1/3 cup sugar, and 1 teaspoon vanilla extract in a small bowl until smooth and creamy. Set aside.
05 - Roll tablespoon-sized portions of dough into balls and place on the prepared baking sheets about 2 inches apart. Use your thumb or the back of a teaspoon to press a deep well into the center of each ball. Fill each well with about 1 teaspoon of the cheesecake mixture.
06 - Bake for 11 to 13 minutes, until cookies are set and the edges are lightly golden. Let cool on the baking sheets for 5 minutes, then transfer to a wire rack.
07 - While the cookies cool, combine the caramel candies and heavy cream in a microwave-safe bowl. Heat in 30-second bursts, stirring between each, until the caramel is melted and smooth.
08 - Drizzle the warm caramel sauce generously over each cooled cookie. Allow the caramel to set before serving.