Heat the oven to 350 degrees.
In a saucepan over low heat, melt the butter, peanut butter, white sugar, and brown sugar together. Do not boil. Just stir until all the butter is melted.
Move the peanut butter mixture to a mixing bowl. Stir in vanilla and eggs. Beat for about 2 minutes on medium.
Mix the batter on low. Slowly add the flour, baking soda, and salt. Blend until the mixture is thoroughly integrated. Stir in the baking chips.
Spoon the batter onto baking sheets and bake at 350 degrees for 10 minutes. The cookies are done when they are no longer shiny. They will not be brown on bottom. Do not overbake.
Cool the cookies on the baking sheet for 20 minutes before moving to the cooling rack. Cool on your cooling rack for at least 5 minutes before enjoying.