Butter a 13- by 9- by 2-inch baking pan, then line bottom of pan with parchment paper and butter parchment.
Preheat oven to 350 degrees F with rack in middle.
Beat together butter and sugar with an electric mixer at medium-high speed until mixture is light and fluffy, then add peanut butter and beat until incorporated.
Beat in whole eggs, egg yolk, and vanilla.
Reduce mixer speed to low, then mix in flour until just combined.
Mix in chocolate chips (1 1/2 cups) then spread batter in baking pan, smoothing top. (It will be thick, almost like cookie batter.)
Bake until brownies are deep golden, puffed on top and a wooden pick inserted in center comes out with some crumbs adhering, 40 to 45 minutes.
Cool completely in pan on a rack, about 1 1/2 hours.
Make ganache: Put chocolate chips (1 1/2 cups) in a heatproof bowl.
Bring cream to a boil in a small saucepan, then pour over chocolate chips and let mixture stand for one minute.
Gently whisk in butter until it is incorporated, chocolate is melted, and a smooth mixture forms.
Spread ganache on cooled brownies and let stand until set, about 15 minutes.