Preheat oven to 375 degrees.
Unwrap squares of chocolate and put them in a microwavable bowl. Melt in microwave, 30 seconds at a time, stirring in between.
Combine butter, brown sugar, and white sugar in a mixing bowl. Beat on medium speed until smooth.
Add baking soda and salt. Beat for another minute or until well mixed. Add the egg and beat until it is well mixed. Add red food coloring and mix until well incorporated.
Scrape the sides of the bowl. Add melted chocolate and mix until well combined.
Scrap sides of bowl. Mix in one cup flour. Mix in sour cream. Add the rest of the flour and mix well. Mix in chocolate chips.
Drop tablespoon sized cookies onto a greased or parchment paper lined cookie sheet.
Bake cookies for 11 minutes or until they rise and become firm. Cool on wire rack.
For the frosting mix butter, cream cheese and vanilla until smooth. Add powered sugar. Adjust powdered sugar for desired spreading consistency. Spread over cooled cookies.