Whisk 2 ¼ cups room-temperature brewed coffee, 2 tablespoons granulated sugar, 1 tablespoon vanilla extract, and 1 tablespoon white rum (if using) together in a medium bowl until the sugar is dissolved.

Place 8 ounces cold mascarpone cheese in the bowl of a stand mixer fitted with the whisk attachment. With the mixer on medium-low speed, stream in 2 ¾ cups cold heavy cream. Increase to medium-high and beat until firm peaks form, about 1 ½ to 2 minutes.

Whisk 1 (14-ounce) can sweetened condensed milk, 1 (3.4-ounce) box instant vanilla pudding mix, 2 teaspoons vanilla extract, and ¼ teaspoon kosher salt together in a medium bowl until thick and not fully dissolved. Scrape into the stand mixer and beat on low speed until just combined, about 30 seconds.

Add ½ cup whole milk and beat on low speed until combined and smooth, about 30 seconds.

Dip each ladyfinger into the soak and place in a 9x13-inch baking dish. Repeat until the bottom is covered with a single layer of ladyfingers.

Peel and slice 2 of the ripe bananas crosswise into thin rounds. Arrange over the ladyfingers.

Scrape half of the mascarpone cream over the layers and smooth into an even layer.

Repeat with a second layer of soaked ladyfingers, sliced bananas, and the remaining mascarpone cream.

Beat 1 ¼ cups cold heavy cream, 2 tablespoons granulated sugar, and ½ teaspoon vanilla extract in the mixer until firm peaks form. Dollop over the mascarpone cream.

Refrigerate until set, at least 5 hours or preferably overnight.

Sprinkle crushed ladyfingers over the whipped cream before serving.