In a large mixing bowl, cream together softened butter, granulated sugar, and brown sugar until light and fluffy, about 3-4 minutes. Beat in the egg and vanilla extract until fully combined.

In another bowl, whisk together all-purpose flour, baking soda, and salt; gradually mix this dry mixture into the wet ingredients until just incorporated.

Gently fold in chopped strawberries into the cookie dough.

Cover the mixing bowl with plastic wrap and refrigerate the dough for at least 30 minutes.

Preheat your oven to 350°F (175°C). Once the dough has chilled, line a baking sheet with parchment paper. Scoop balls of cookie dough, spacing them about 2 inches apart.

Bake for 10 to 12 minutes, until edges are golden brown. Allow cookies to cool on the tray for about 5 minutes.

In a mixing bowl, whip together cream cheese, powdered sugar, and vanilla extract until smooth. Frost the cooled cookies generously.