Heat oven to 375° F. In a small bowl, whisk together flour, baking soda and salt. In a large bowl with an electric mixer, cream butter, vegetable shortening, granulated sugar, brown sugar and vanilla extract.
Add eggs, 1 at a time, beating well after each addition. On low speed, beat in flour mixture. By hand, stir in white and milk chocolate chips, mint chips and walnuts.
Drop rounded tablespoons of dough onto ungreased baking sheets. Bake at 375° F for 10 to 12 minutes or until golden brown. Cool on baking sheets for 5 minutes; remove to wire racks to cool completely.