Preheat oven to 350 degrees F. Coat a 9x5-inch loaf pan with nonstick cooking spray or butter, or line with parchment paper for easy removal.
Using a stand mixer fitted with the paddle attachment (or a large mixing bowl with a hand mixer), combine the butter, brown sugar, sugar, eggs and vanilla and beat until combined.
In a separate bowl, combine the flour, baking powder, baking soda andsalt. Mix well. Gradually add to the butter mixture and beat on medium-low speed until just combined.
Fold in the mashed bananas, then gently stir in 1 3/4 cups of the chopped peanut butter cups.
Pour the batter into the prepared loaf pan and spread in an even layer. Sprinkle the remaining 1/4 cup chopped peanut butter cups over the top.
Bake in the preheated oven for 50-60 minutes, or until a toothpick inserted into the center comes out clean. Let sit in the pan for 10 minutes before removing and serving.