Instructions

Before you deal with the tuna, you need to arrange your curing set-up. First, you'll need a baking dish or another vessel with raised sides that holds the piece(s) of tuna that will also allow you to place another slightly smaller baking dish, pan, or cutting board in it.
Rinse off the tuna and make sure there aren't any bits of skin still attached to it (unlike cured salmon, tuna cures best without its thick skin attached). Pat it thoroughly dry and set it in the baking dish.
In a small bowl, combine the salt, sugar, and pepper. Sprinkle the fish all over with the vodka or aquavit, then coat it all over with the salt-sugar-pepper mixture. It will seem like a lot, but pat as much of it to stick to the fish as possible.
Lay a piece of plastic wrap on top of the fish, laying it down into the pan and loosely tucking it around the fish. Top that with another piece of plastic wrap or foil and tuck it loosely around the outside edge of the pan. Set a baking dish, pan, or cutting board on top of that. Place the whole set-up in the fridge and then weigh it down with a small heavy pot or several cans. The salt and sugar will draw water out of the fish and cure it, and the weight will help condense the flesh, creating a unique silky texture. Leave it in the fridge for at least 12 hours and up to 24.
The tuna will now be ready to eat, although I like to turn the fish after 12 to 24 hours, replace it in the dish with the weights, and let it sit another 12 to 24 hours.
When ready to eat, remove the tuna, brush off as much of the salt-sugar mixture as you can (you can rinse it all off, if you're so inclined, just be sure to pat it thoroughly dry afterward). Use a sharp knife to cut very thin slices of the cured tuna for serving.