In a medium bowl, beat the cream cheese and powdered sugar until smooth. Scoop tablespoon-sized portions onto a parchment-lined baking sheet and freeze for about 1 hour, or until firm.
In a large bowl, combine melted butter, softened cream cheese, granulated sugar, and brown sugar. Mix until creamy. Add the egg and blend until incorporated. Stir in flour, baking soda, and salt until dough forms. Gently fold in chopped strawberries. Chill dough for 30 minutes.
Preheat oven to 350°F (175°C). Line baking sheets with parchment. Scoop 2 tablespoons of dough, flatten slightly, and create a small well. Place frozen cream cheese filling in the center, cover with another tablespoon of dough, and seal edges completely.
Arrange cookies 2 inches apart on the sheet. Bake for 15–17 minutes, rotating halfway through. Edges should be golden and centers just set.
Cool cookies on the sheet for 10 minutes before transferring to a rack. Serve warm for gooey centers or chilled for a firmer texture.
