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1
Start a charcoal or wood fire or preheat a gas grill or broiler.
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2
In a medium bowl or blender, add lime juice, soy sauce, olive oil, sesame oil, pepper and 2 tablespoons water.
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3
Whisk or blend until emulsified.
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4
Soak greens in this mixture while preparing the tuna.
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5
Using a sharp, thin-bladed knife like a boning knife, make a small horizontal incision halfway down any side of the tuna steak.
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6
Insert the knife almost to the opposite edge of the steak, then swing it back and forth, turning the knife as necessary to keep the blade facing the direction you're cutting.
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7
The goal is to create a large pocket.
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8
Be careful not to cut through the top, bottom or opposite edge of the tuna, and try to keep the entry point relatively small.
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9
Drain the greens of excess marinade and cram them into the pocket; you can overstuff as long as you don't tear the tuna (the tuna won't shrink, nor will the greens expand).
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10
If the pocket opening is small, seal it with a toothpick; if it's more than an inch or two wide, use two skewers.
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11
Marinate the tuna in the remaining soy mixture until the grill is hot, or up to an hour at room temperature or several hours refrigerated.
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12
Grill the tuna, turning once, a total of about 6 minutes an inch of thickness (if your steak is 1 1/2 inches thick, for example, turn it after about 4 minutes and cook 4 or 5 minutes more).
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13
Season with salt and pepper, cut into 1/2-inch-thick slices and serve.
