**Prepare the Cheesecake Filling:**
In a small bowl, beat the cream cheese, powdered sugar, and vanilla extract until smooth. Scoop teaspoon-sized portions onto a parchment-lined plate and freeze for at least 30 minutes.
**Make the Cookie Dough:**
In a mixing bowl, beat the butter and sugar together until light and fluffy, about 2-3 minutes. Add the egg, vanilla extract, and almond extract, mixing until combined.
**Combine Dry Ingredients:**
In a separate bowl, whisk together the flour, baking powder, baking soda, salt, and crushed freeze-dried strawberries. Gradually add the dry ingredients to the wet ingredients, mixing until a soft dough forms.
**Assemble the Cookies:**
Scoop a tablespoon of cookie dough and flatten it slightly in your palm. Place a frozen cheesecake filling ball in the center, then fold the dough around it, sealing the edges. Roll into a ball and place on a baking sheet lined with parchment paper.
**Bake:**
Preheat your oven to 350°F (175°C). Bake the cookies for 10-12 minutes, or until the edges are set and the tops are just barely golden.
**Cool:**
Allow the cookies to cool on the baking sheet for 2-3 minutes before transferring them to a cooling rack. Dust with powdered sugar if desired.