Tuna bellies, or toro, are prized in sushi bars for their velvety texture. That said, you can also use tuna loin in this recipe; it will simply be a little lean. Make sure that your knife is very sharp--it's the key to slicing through the soft fish easily without tearing it.
1. Combine 2 tbsp. salt and the sugar in a small bowl. Rub both sides of tuna belly with salt mixture. Set on a plate, cover, and chill at least 6 hours and up to overnight.
2. Briefly rinse fish with cold water and pat dry with paper towels. Using a very sharp knife, thinly slice belly diagonally across the grain, pulling the knife through the fish rather than sawing. Divide slices among 4 to 6 small salad plates, spreading them out in a single layer. Cover each with plastic wrap and, using the bottom of a liquid measuring cup, gently pound fish into a thin layer.
3. Thinly slice radishes, then cut into thin matchsticks. Transfer to a small bowl and add avocado, chives, oil, and lemon juice. Season with remaining 1/2 tsp. salt and toss until well combined. Spoon some salad onto each plate.