Cut the tuna into 18 cubes, each one 1/2-inch thick, and 1 1/4-inch square. Place the cubes between sheets of lightly-oiled wax paper and flatten with a cleaver. You will have 18 very thin, fairly round "scallops" of tuna. Divide among 6 dinner plates and chill.
Prepare the sauce: Put the egg yolks in a food processor. Add the lemon juice, and blend for 3 seconds. Add the oil, by drops, at first, then in a thin stream. The sauce will be fairly thick. Add the basil, blend for 3 seconds, then add the cream. Season to taste with salt and pepper. Refrigerating for 30 minutes brings out the flavor.
When ready to serve, pour the sauce over the tuna slices. Shave the white truffle over all, and garnish each plate with fresh basil leaves.
Note: Fresh white truffles from Piedmont are available in the U.S. from September through December. They are hideously expensive. The dish also works without them, or with extra-thin slices of white mushrooms sprinkled over the tuna.