01 - Preheat oven to 350°F. Line two baking sheets with parchment paper and set aside.
02 - In a large 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 just combined. Do not overmix. Cover the dough and refrigerate for 20 minutes to firm up.
04 - While the dough chills, beat the softened cream cheese, 1/3 cup granulated sugar, and 1 teaspoon vanilla extract in a small bowl until smooth and creamy. Set aside.
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 or the back of a teaspoon into the center of each ball to create a deep well.
06 - Fill each well with approximately 1 teaspoon of the cheesecake filling, smoothing the top gently.
07 - Bake for 11-13 minutes, or until the cookie edges are set and lightly golden. Allow cookies to rest on the baking sheets for 5 minutes before transferring to a wire cooling rack.
08 - In a microwave-safe bowl, combine the caramel candies with 1 tablespoon heavy cream. Microwave in 30-second intervals, stirring between each, until the caramel is completely smooth and pourable.
09 - Drizzle the warm caramel sauce over each cooled cookie. Allow the caramel to set at room temperature before serving. Optionally sprinkle with flaky sea salt for added flavor.