Preheat oven to 375 degrees F. In a large mixing bowl beat butter with an electric mixer on medium to high speed for 30 seconds. Add sugars, baking soda, and salt. Beat until combined, scraping sides of bowl occasionally. Beat in eggs and vanilla until combined. Beat in as much of the flour as you can with the mixer. Stir in any remaining flour. Stir in chocolate pieces and cherries.
Drop dough by tablespoons 2 inches apart onto ungreased cookie sheets. Bake 9 minutes. Transfer to racks. Cool. Makes 6 dozen cookies.