Pre-heat the oven to 350° F, and grease a 9x13 baking pan.
Cream together (or mix together) the butter, sugar, and brown sugar 'til the mixture is light and fluffy.
Add in the egg, peanut butter, and vanilla extract, mixing well.
In a separate bowl, whisk together the flour, baking soda, and salt.
Gradually mix the dry ingredients and the oats into the creamed mixture.
Spread the cookie mixture in the prepared 9x13 baking pan.
Bake at 350° F for about 20-25 minutes, or 'til a toothpick inserted in the center comes out clean.
Upon removal from the oven, sprinkle chocolate chips over the top, and let stand for about 5 minutes.
Then spread the melted chocolate over the top.