Preheat your oven to 350°F (175°C).
In a large bowl, cream together the softened butter, cream cheese, granulated sugar, and brown sugar until smooth.
Add in the vanilla extract and mix well.
In a separate bowl, whisk together the flour, baking soda, and salt.
Gradually add the dry ingredients to the wet mixture, mixing until just combined.
Fold in the pureed strawberries gently.
Drop rounded tablespoons of dough onto a baking sheet lined with parchment paper, spacing them about 2 inches apart.
Bake for 12-15 minutes, or until the edges are lightly golden.
Remove from the oven and let cool on a wire rack.
Once cooled, mix powdered sugar with a bit of strawberry puree to create a frosting and spread it on top of each cookie.