In a large bowl, cream together butter and peanut butter. Add granulated and brown sugars, then beat until fluffy, about 1 minute. Add the egg, milk, and vanilla. Beat for another minute.
In a separate bowl, sift together the flour, baking soda, and salt.
Gradually stir dry ingredients into butter mixture until just combined.
Cover bowl or wrap dough in wax paper. Chill for at least 1 hour (up to 24 hours) in the refrigerator. Refrigerating will help the flavors meld and also create a firmer dough to roll into balls.
Preheat oven to 375 degrees and line a baking sheet with parchment paper. Set aside.
Remove dough from refrigerator and shape by hand into 1 inch balls. Roll balls in white sugar.
Place cookie dough balls 2 inches apart onto a parchment lined baking sheet. Press a fork into the balls, creating a crosshatch pattern. Bake for 9-11 minutes, or until lightly browned around edges. Allow to cool for 5 minutes before removing to a wire rack to cool completely.
Your cookies will keep for 5-7 days in a sealed container. To help keep cookies fresh, you can place a slice of bread in the container with the cookies. Replace the bread slice as needed.
You can keep raw cookie dough in the refrigerator for 3 days. Cookie dough balls (and baked cookies) freeze well, up to 3 months in a sealed plastic container or freezer bag. Allow frozen balls to thaw for up to 10 minutes on the baking sheet before baking, or add 1-2 minutes to the baking time.