Preheat the oven to 325 degrees. Move the rack to the lower third of the oven. Coat an 8x8-inch baking pan with cooking spray or butter. Line it with parchment paper with the ends hanging over the sides.
In a large heat-proof bowl, combine the butter, sugar, cocoa, and salt. Set the bowl in a large skillet of water and simmer over medium-low heat. Stir occasionally until the butter is melted and the mixture is hot to the touch. The mixture will look slightly grainy.
Remove from heat and cool until warm.
Add vanilla and stir with a wooden spoon.
Add the eggs one at a time, mixing thoroughly after each one. When the batter looks well blended, smooth, and shiny, slowly add the flour and stir until combined thoroughly, then stir vigorously for 30 strokes.
Stir in the peanut butter chips.
Pour into the baking pan and place a few more peanut butter chips on top. Side Note: The batter will be thick.
Bake the brownies for 20-25 minutes, or until a toothpick inserted in the center comes out clean.
Let cool completely, then lift the ends of the parchment paper and transfer the brownies to a wire cooling rack to cool before slicing and serving. Enjoy.