Prepare the Cheesecake Filling: In a medium bowl, mix the cream cheese, sugar, vanilla extract, and strawberry jam or puree until smooth. Cover and refrigerate.
Make the Cookie Dough: Cream together the softened butter, granulated sugar, and brown sugar until light and fluffy. Blend in the egg and vanilla extract.
Combine the Dry Ingredients: Whisk together the flour, baking soda, baking powder, and salt. Gradually add to the wet ingredients and mix until smooth. Fold in the crushed freeze-dried strawberries.
Chill the Dough: Cover the dough with plastic wrap and refrigerate for 30 minutes.
Assemble the Cookies: Preheat oven to 350°F (175°C). Scoop out about 1 tablespoon of dough, flatten it, add ½ teaspoon of cheesecake filling, and seal with another tablespoon of dough. Place on a baking sheet.
Bake the Cookies: Bake for 12-15 minutes until edges are golden. Let cool on the baking sheet for 5 minutes before transferring to a cooling rack.