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 the speed to medium-high and beat, scraping the bowl as needed with a flexible spatula, until firm peaks form, 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. It will be thick and the pudding will not be completely dissolved. Scrape into the stand mixer and beat on low speed until just combined.

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

Dip each ladyfinger quickly in the soak and place in a 9x13-inch baking dish until the bottom is covered.

Peel and slice 2 of the ripe medium bananas crosswise into thin rounds and arrange in a single layer over the ladyfingers.

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

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

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

Refrigerate until the tiramisu is well-chilled and set, at least 5 hours.

Sprinkle crushed ladyfingers over the whipped cream before serving.