Preheat oven to 350 degrees F (176 C). Line a couple of cookie sheets with parchment paper or leave ungreased/un-lined.
Beat the butter and both sugars together. Beat in the peanut butter and egg; Scrape sides of bowl and beat in the salt, baking soda and vanilla. When well blended, add flour and stir until it is blended. Stir in the chips if using.
Shape dough into 1-inch balls (or scoop with a 1 tablespoon size cookie scoop) and arrange on cookie sheets about 2 inches apart. At this point you can roll them in sugar or sprinkle sugar of the top if you'd like. Flatten balls with a fork dipped in sugar (which never sticks, so I prefer lightly dampened with water) to make criss-cross patterns; Bake for 10 minutes or until lightly browned around the edges.
**If you only have salted butter you can use that, but reduce the salt in the recipe to about ¼ teaspoon.
**If you have some, try adding about ¼ teaspoon of chipotle powder to the batter.