You need a large 9×13-inch baking pan/dish.
Whisk the coffee and rum together in a shallow bowl. Set aside.
Working one at a time, dip ladyfingers into the coffee mixture just long enough to get them wet, do not soak it! Arrange the dipped ladyfingers in the baking pan to make one solid layer. If needed, cut some ladyfingers to fill in any empty spaces.
Spoon half the mascarpone cream filling over the ladyfingers. If desired, dust some cocoa powder over the cream, this is optional, but I like the extra cocoa in my tiramisu.
Dip remaining ladyfingers into the remaining coffee mixture and arrange one-by-one on top of the mascarpone layer.
Spread the remaining mascarpone mixture evenly on top. Refrigerate for 2 hours, then dust with cocoa, cover with plastic wrap and refrigerate at least 4 hours. Overnight is best.
Using a sharp knife, slice chilled tiramisu into servings. Wipe knife clean between cuts. A small metal serving spatula is very helpful for removing the slices.