Preheat the oven to 350 degrees F and place an oven rack in the middle position. Lightly grease the bottoms of three 8-inch cake pans with baking spray or butter, and cover with parchment rounds. Set aside.

In a medium bowl, whisk the flour, baking powder, and salt. In a separate small bowl, combine the bananas, vanilla, and rum.

In a stand mixer fitted with the paddle attachment, cream the butter and sugar on low speed for 5 minutes. Add the eggs, one at a time, allowing each egg to incorporate before adding the next. Scrape down the sides of the bowl. With the mixer still on low speed, swiftly alternate between adding the dry and wet ingredients for a minute. Scrape down the sides, making sure to reach the bottom of the bowl. Turn the mixer up to medium speed for 30 seconds.

Distribute the batter evenly among the three cake pans, using a spatula to even out the tops.

Bake until a toothpick inserted into the center of each cake comes out clean, 29 to 33 minutes. Allow the cakes to cool completely in the pan before removing.

To form the syrup, add the sugar and water to a medium saucepan. Cover and turn the heat to high. Once the liquid begins to simmer and is giving off steam, remove the cover (this helps prevent crystallization). Using a candy thermometer, cook the sugar to the soft-ball stage, 235 to 240 degrees F, approximately 5 minutes.

While the sugar is turning to syrup, beat the egg whites on high speed in a stand mixer with the whisk attachment, until a soft peak has formed.

Turn the mixer speed down to medium-low and very slowly pour the syrup down the side of the bowl into the egg whites. Don’t pour the hot syrup directly into the meringue or the egg whites might scramble.

Once the syrup is completely incorporated, turn the speed to high and allow the meringue to continue to form a stiff peak while cooling to room temperature, 15 to 20 minutes. To speed up this process, ice packs may be placed around the bowl.

Once the meringue has come to room temperature, slowly begin incorporating the soft butter on medium speed. Once all the butter has been mixed, turn the mixer speed up to high and slowly add the vanilla, followed by the peanut butter, 1 tablespoon at a time. After adding in 1/2 cup, taste the buttercream for flavor. Add additional peanut butter to taste, 1 tablespoon at a time.

Place a cardboard round on the cake stand and top with the first layer of cake (remove the parchment paper).

Spread approximately 1 cup of buttercream evenly on the cake with a spatula. Repeat with the second and third layers (don’t forget to remove the parchment each time). Use an offset spatula to apply a thin layer of frosting to the side and top of the cake. Chill in the refrigerator for 30 minutes to set this first layer of buttercream. Cover the entire cake with a final layer of frosting and place in the refrigerator to chill.

Place the chocolate and butter in a medium heatproof bowl over a pot of simmering water.

Using a heatproof spatula, stir the mixture until melted and smooth.

Allow the glaze to cool for 2 to 3 minutes. Starting at the center and moving outward in a circular motion, pour the glaze over the chilled cake, smoothing the top with a small offset spatula.

Serve the cake at room temperature.