Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.
In a large bowl, cream together the butter, granulated sugar, and brown sugar until light and fluffy. Beat in the egg and vanilla extract.
In a separate bowl, whisk together the flour, baking soda, and salt. Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
In a medium bowl, beat together the cream cheese and powdered sugar until smooth. Gently fold in the cherry pie filling.
Drop rounded tablespoons of cookie dough onto the prepared baking sheets. Make a well in the center of each cookie and fill with a spoonful of cheesecake filling.
Bake for 10-12 minutes, or until the edges are lightly golden brown. Let cool on the baking sheets for a few minutes before transferring to a wire rack to cool completely.
Notes
Enjoy these cookies warm or at room temperature. Store in an airtight container.