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 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. 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.

Quickly dip and submerge one ladyfinger in the soak and place in a 9x13-inch baking dish. Repeat until bottom is covered in a single layer of ladyfingers, 20 to 22.

Peel and slice 2 of the ripe medium bananas crosswise into thin rounds. Arrange 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 remaining mascarpone cream over the top.

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

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

When ready to serve, sprinkle 3 to 4 crushed ladyfingers over the whipped cream and scoop or cut into squares.