Preheat the oven to 350 degrees F. Spray a 9×5 inch loaf pan with cooking spray.
In the bowl of a stand mixer with the flat beater attached, cream butter, brown sugar, peanut butter and vanilla on medium-high speed until light and fluffy, 1 to 2 minutes. Add the flour and mix at low speed until well combined, about 1 minute (the mixture will be crumbly)
Press mixture into the bottom of the prepared loaf pan. Bake at 350 degrees for 12-15 minutes or until set and lightly browned. Transfer to a wire rack to cool while you make the filling.
To make the filling in a small saucepan over low heat, cook and stir the milk and butter until mixture comes to a boil and thickens. Remove from the heat; stir in peanuts and vanilla. Spread evenly over crust.
Bake for 15-17 minutes or until set. Immediately sprinkle with chocolate chips; let stand for a few minutes to soften, then spread over filling. Sprinkle with peanuts. Cool completely on a wire rack. Cut into bars.