Line a large, rimmed baking sheet with parchment paper or a nonstick mat. Set aside.
Place the butter, light brown, and white sugar into a large mixing bowl, and whisk for 2-3 minutes until smooth and fluffy. Add egg and vanilla to the bowl and continue whisking until smooth and combined. Add flour, baking soda, and baking powder to the bowl. Gently fold in the flour until the mixture is combined and smooth. Fold in strawberries.
Use an ice cream scoop to divide the mixture into 12 and shape it into balls. Place the cookie dough balls onto the lined baking sheet. Use the back of a spoon or your fingers to form an indent in the center of each one. Place the baking sheet with the cookies into the refrigerator to chill for 30 minutes.
After 30 minutes, preheat oven to 350°F/180°C/Gas 4.
While heating the oven, make the cheesecake filling by whisking the cream cheese and powdered sugar in a small bowl until smooth and fluffy.
Remove the cookies from the refrigerator and fill the indents with the cream cheese mixture.
Bake the cookies for 13-15 minutes until golden and puffed. Remove from the oven and set aside to cool for 10 minutes.
Drizzle the cookies with warm jam and serve immediately. Enjoy!