In a medium bowl, whisk together gluten free all-purpose flour blend, baking powder, and salt. Set aside.
In a large bowl, beat softened butter, cream cheese, and granulated sugar with an electric mixer until smooth and creamy, about 3 minutes. Beat in the egg and vanilla extract until combined.
Add the flour mixture and mix on low speed until just combined. Fold in the crushed freeze-dried strawberries and white chocolate chips with a spatula. The dough will turn a beautiful pink color. Cover and refrigerate for at least 1 hour.
Preheat your oven to 350 degrees F and line two baking sheets with parchment paper. Scoop rounded tablespoons of dough, roll into balls, and place 2 inches apart on the prepared baking sheets.
Bake for 11 to 13 minutes until the edges are set but the centers are still soft and slightly puffy. Let the cookies cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.
For the drizzle, melt 1/4 cup white chocolate chips with coconut oil in a microwave-safe bowl, stirring every 20 seconds until smooth. Drizzle over the cooled cookies using a fork or spoon in a zigzag pattern. Let the drizzle set for 10 minutes before serving.