Start by brewing the coffee and pouring it into a wide, shallow bowl. Stir in 2 tablespoons of rum if you are using it, then whisk until blended. Take out a 9×9-inch serving pan and set everything aside.
Separate the egg whites from the yolks. Add the whites to the bowl of a stand mixer fitted with the whisk attachment, and place the yolks in a small bowl for later. Beat the whites on high speed until foamy, then, with the mixer still running, slowly pour in 1/3 cup of the granulated sugar. Keep beating on high until stiff peaks form, about 3 to 5 minutes. Using a silicone spatula, transfer the meringue to a separate large bowl and set aside.
Place the reserved egg yolks and the remaining ⅓ cup of granulated sugar into the stand mixer bowl, no need to wash it first. Using the whisk attachment, beat on high speed until the mixture turns light and pale in color, about 2 minutes.
Pause the mixer and scrape down the sides and bottom of the bowl. Add the mascarpone, the remaining 2 tablespoons of rum, the vanilla extract, and the salt. Whisk until everything is blended, about 20 seconds. Then remove the bowl from the stand mixer.
Transfer half of the meringue into the bowl with the egg yolk mixture. Using a silicone spatula, gently fold until just combined. Add the remaining meringue and continue folding until no white streaks remain. Spread a light layer of this mascarpone cream across the bottom of the baking pan.
Briefly dip the ladyfingers into the coffee mixture on both sides, since they will break apart if left too long. Arrange them in a single layer across the bottom of the baking pan. Spread about half of the mascarpone cream over the ladyfingers and smooth it into an even layer.
Repeat with a second layer of coffee-dipped ladyfingers. Finish by adding the remaining mascarpone cream on top and spreading it out into a smooth, even layer.
Set the pan in the refrigerator, uncovered, for at least 4 hours or up to overnight. If chilling longer than 4 hours, leave it uncovered for the first 4 hours, then gently cover with plastic wrap, making sure it does not press into the mascarpone cream since it will stick.
When you’re ready to serve, take the tiramisu out of the fridge. Generously dust the top with cocoa powder, then slice and serve.
