While oven is preheating, lightly grease a 9x13 inch pan (unless you're using a nonstick pan).
In medium-large mixing bowl, use an electric mixer on high speed to cream together the butter, peanut butter and sugars.
Lower the speed to medium, and add the eggs in one at a time, as well as the vanilla, beating well between each ingredient.
Then, stir in the remaining ingredients, mixing by hand until everything is uniformly blended.
Pour the batter into the greased pan, and bake on the center oven rack for 15 to 20 minutes or until the top feels firm and a toothpick inserted into the center comes out clean.
Cut while still hot, but let brownies cool in pan for at least 30 minutes prior to serving.