Preheat the oven to 350 F. In a medium bowl, whisk together flour, salt, and baking soda. In a large bowl, combine butter with both sugars until fluffy. Add in egg and vanilla extract, and mix until smooth.
Add in the flour mixture, mix until it is fully combined. Fold in the chocolate chips. Evenly press the cookie dough into a greased round 9-inch cake pan. Bake for 20-25 minutes. Let cool completely.
In a large bowl, mix the butter with powdered sugar, vanilla extract, and milk until smooth. Remove about 1/2 cup frosting in a piping bag and set aside.
Add cocoa powder to the remaining frosting until smooth. Cut a long strip of the cookie cake in the middle and remove. Push the remaining cookie cake together to form a oval shape.
Evenly spread the chocolate frosting onto the cake. Decorate the cookie cake with the vanilla frosting in a football pattern.
