1. Coat 2 large baking sheets with nonstick cooking spray.
2. In bowl, beat together butter, peanut butter and sugars until smooth and fluffy, about 3 minutes. Add egg and vanilla; beat 1 minute.
3. In medium-size bowl, whisk together flour, baking soda and salt.
4. On low speed, alternately beat flour mixture and milk into butter mixture, beginning and ending with flour; beat 1 minute. Fold in chips and nuts. Cover; refrigerate 15 minutes.
5. Heat oven to 350 degrees F. Drop dough, about a scant 1/4 cup per cookie, onto prepared sheets, about 3 inches apart. Flatten to 1/2-inch thickness.
6. Bake in 350 degree F oven until puffed and slightly browned around edges, 16 to 18 minutes. Cool on sheets 2 minutes. Remove to rack; let cool. Makes 18 cookies.