Preheat oven to 350º.
Combine flour, cocoa powder, baking soda, and salt in a mixing bowl, and set aside.
In a large mixing bowl, cream butter and sugars together until light and fluffy.
Beat in egg and vanilla extract until completely combined.
Beat in flour mixture, half at a time.
Stir in chocolate chips.
Scoop by the heaping tablespoon onto a parchment lined baking sheet with at least 2 inches between them.
Pat down to flatten somewhat.
Bake in center of oven for 10 minutes, or until cookies are just barely set.
Remove from oven and transfer to a wire rack to cool.
While cookies are cooling, combine cream cheese and strawberries.
Beat until strawberries are mostly incorporated, and cream cheese has turned pink.
Beat in powdered sugar.
Use a knife or pastry bag to ice cookies.