In a small bowl, beat the softened cream cheese, powdered sugar, and vanilla extract until completely smooth. Line a small tray with parchment paper. Scoop small teaspoons of the mixture (about 12 dollops) onto the tray. Place the tray in the freezer for at least 20-30 minutes until the dollops are firm enough to handle.

In a large mixing bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy. Add the egg and vanilla extract, beating until well combined. In a separate bowl, whisk the flour, baking soda, and salt. Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Gently fold in the finely chopped strawberries and white chocolate chips if using.

Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper. Take a large scoop of cookie dough (about 2 tablespoons) and flatten it in your palm. Place one frozen cream cheese dollop in the center. Carefully wrap the dough around the filling, pinching the edges to ensure the cheesecake is fully sealed inside. Roll it into a smooth ball.

Place the stuffed dough balls on the prepared baking sheet, spacing them at least 2 inches apart. Bake for 10 to 12 minutes, or until the edges are just set and very lightly golden. The centers should still look slightly soft. Allow the cookies to cool on the baking sheet for 10 minutes before transferring them to a wire rack. Cooling is essential to let the cheesecake center set perfectly.