In a large bowl, combine butter, peanut butter, powdered sugar, and vanilla. Beat with an electric mixer until smooth. Dough will be thick and slightly crumbly.
Line a 9×13-inch pan with parchment paper. Press the peanut butter mixture firmly into an even layer.
Combine chocolate chips and 1 tbsp butter in a microwave-safe bowl. Microwave in 30-second intervals, stirring between, until melted and smooth (~1½ min).
Pour melted chocolate over the peanut butter layer and spread evenly.
Let sit at room temperature 30–60 minutes until chocolate sets.
Lift bars using parchment paper, transfer to a cutting board, and slice with a sharp knife.
Refrigerate for at least 1 hour before serving.