Cream together the softened butter, cream cheese, granulated sugar, and brown sugar until light and fluffy. Beat in the egg yolk and vanilla extract until well combined.

In a separate bowl, whisk together the all-purpose flour, baking powder, and salt. Gradually add the dry ingredients to the wet mixture, mixing until just combined. Fold in the crushed freeze-dried strawberries.

Cover the cookie dough and chill in the refrigerator for at least 30 minutes.

While the dough chills, prepare the cheesecake filling by beating together the softened cream cheese, powdered sugar, and vanilla extract until smooth and creamy.

Scoop out portions of cookie dough, flatten each slightly, and place a small dollop of the cheesecake filling in the center. Carefully enclose the filling with the cookie dough, forming a ball.

Place the assembled cookies on a prepared baking sheet and bake in a preheated oven at 350°F (175°C) for 10-12 minutes, or until the edges are lightly golden.

Allow the cookies to cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.