In a large mixing bowl, beat the butter and peanut butter with an electric mixer for 30 seconds. Add the sugars, baking soda and salt. Beat until combined, scraping sides of the bowl occasionally.
Beat in egg, milk and vanilla. Using the mixer, beat in as much of the flour as you can. Stir in remaining flour by hand. Stir in the chocolate pieces, peanuts and peanut butter cups.
Drop by generously rounded teaspoons 2 inches apart onto an ungreased cookie sheet. Bake the cookies in a 350 degree oven for about 10 minutes or until lightly browned. Transfer cookies to a wire rack to cool. Makes about 30 cookies.
If you like, for easier chopping, freeze miniature chocolate-covered peanut butter cups in their wrappers for 1 hour. Remove frozen candies from wrappers before chopping.