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, scraping down the sides of the bowl as needed, about 30 seconds total.

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

Working with 1 ladyfinger at a time, quickly dip and submerge in the soak and place in a 9x13-inch baking dish (at least 2 ½ inches tall). Repeat until the bottom is covered in a single layer of ladyfingers, 20 to 22.

Peel and slice 2 of the ripe medium bananas crosswise into thin ⅛- to ¼-inch-thick rounds. Arrange in a single layer over the ladyfingers.

Scrape half of the mascarpone cream (about 4 ⅓ cups) 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, making sure the bananas are completely covered.

Beat 1 ¼ cups cold heavy cream, 2 tablespoons granulated sugar, and ½ teaspoon vanilla extract in the stand mixer with the whisk attachment on medium-high speed until firm peaks form, 1 ½ to 2 minutes. Dollop over the mascarpone cream and smooth or swoop over the top as desired.

Refrigerate until the ladyfingers are soft and the tiramisu is well-chilled and set, at least 5 hours but preferably overnight. Loosely cover with plastic wrap if chilling overnight.

When ready to serve, sprinkle 3 to 4 crushed ladyfingers over the whipped cream. Use a big serving spoon to scoop, or use a knife to cut into squares to serve.