Preheat oven to 350 degrees.
Beat the butter and peanut butter together until well mixed. Add the sugars and beat until smooth.
Add the egg and mix well. Add the milk and vanilla. Mix well.
Add the flour, baking soda, baking powder and salt. Mix.
Roll into balls and place on an ungreased cookie sheet. You can roll the cookie balls in a bowl of sugar, if desired - but it's optional.
Gently flatten the cookies with the back of the fork a couple of times, crossing over each other.
Bake for 10-12 minutes.
Let cook for a minute or two, then, if using, place the Dove chocolate in the middle of the cookie.
Let cool completely so that the chocolate doesn't get smooshed if you're going to put them in a container for later. If you need the chocolate to set quicker, place in the refrigerator.