Lightly grease an 8 x 8 pan and line with parchment paper.
Use a standing mixer and beat the butter until creamy.
Add the brown sugar and continue to mix.
Add the peanut butter, crushed graham crackers, vanilla, and salt and mix till combined.
Add the powdered sugar and mix until just combined.
Take the peanut butter mix and press into the lined 8 x 8 pan and gently press until the whole surface is covered and even. You can use the bottom of a measuring cup to even it all out.
Combine the chocolate chips and the heavy whipping cream in a microwave safe bowl. My favorite cups for melting chocolate are these. Microwave in 30 second increments, stirring in between heating. The chocolate will become completely smooth. Stir in the vanilla extract. Pour over the peanut butter bars and use a spatula to evenly cover.
Put the entire pan in the fridge for 1-2 hours. The longer you wait, the more firm they will be for cutting. Remove from fridge and lift the parchment paper from the pan. Cut into squares and serve! Keep these bars refrigerated for up to one week.