Light the grill: Place a chimney starter on the grate of a charcoal grill. Add newspaper in the bottom, then fill with charcoal. Light the newspaper, which will light the charcoal. When the charcoal is mature with ashed-over gray embers (about 30-45 minutes later), remove the grill top and place the charcoal underneath.While you're waiting for the charcoal to heat up, prepare the aioli (Step 2).
Sesame aioli: In a mixing bowl, whisk vinegar, egg yolk, yuzu kosho, and miso to a thick paste. Add the honey, then slowly whisk in the sesame oil and the grapeseed oil, a little at a time, alternating between the oils to balance the aioli. Finish by whisking in the zest from 1 lime and the crème fraîche. Set aside. (Sesame aioli will keep in the refrigerator 2-3 days.)
Tuna burgers: Cut the tuna into thin planks, then into strips and chunks. Finish by roughly chopping to a fine dice. (Alternatively, tuna can go in a meat grinder.) Use a Microplane to grate the ginger (with skin), garlic, lime (zest only), and chile (stopping before you get to the seeds); add them to the chopped tuna. Add the cilantro, followed by half of the aioli, and gently mix to combine. Mix until mixture is tight and sticky, about 3–4 minutes. Chill for 35-40 minutes.
Cook the burgers: Roll the chilled tuna into balls, then gently flatten to just under an inch thick, but don't pack them too tightly. Set patties aside as they're formed. When all the patties are ready to go, season with salt and pepper; grill over medium heat until just cooked through, 3–4 minutes per side.
Assemble the burgers: Place each burger onto a bun; top with sesame aioli and a slice of tomato just before serving.