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 light and fluffy, about 2-3 minutes. 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 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 until smooth and creamy with no lumps remaining.
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 create a deep well. Fill each well with approximately 1 teaspoon of the cheesecake mixture.
06 - Bake for 11-13 minutes, until the cookies are set and the edges are lightly golden. 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 caramel 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. For extra flavor, finish with a light sprinkle of flaky sea salt.