Prepare the Slaw

1. In a medium bowl, large enough to hold the slaw, whisk the rice vinegar, olive oil, sesame oil, soy sauce, honey and ginger. 
2. Add the shredded carrots and sesame seeds and toss to combine. Set aside while you cook the tuna burgers. Slaw can be made several hours ahead and kept, covered, in the fridge.

Prepare the Tuna Burgers

1. Cut the tuna steaks into large (¾-inch) dice and transfer to the bowl of a food processor fitted with the chopping blade. Add the soy sauce, olive oil, sesame oil, egg white, ginger, scallions and garlic. Pulse until you get a rough chop, being careful not to overprocess. 
2. Form the mixture into 4 patties, place them on a plate, cover with plastic wrap and chill in the fridge for at least 30 minutes and up to 6 hours. Chilling the patties will help firm them up so they hold together when you grill or pan sear them. 
3. When ready to cook, preheat the grill to medium-high, if grilling. Otherwise, heat a large skillet (preferably cast iron) over medium-high heat for a minute or so. 
4. Brush the tops of the tuna patties with olive oil. Use a spatula to transfer the patties, oiled-side down, to the grill or skillet and cook for 1 minute per side for rare, 2 minutes per side for medium-rare, or 3-4 minutes per side for medium. I like them cooked until just barely pink in the middle, about 3 minutes per side. Note that if they go directly from the fridge to the fire, they will need an additional minute of cooking time. 
5. During the last minute of grilling time, add the buns, cut-side down, to the grill, to toast (or toast in the toaster oven).
6. If using kewpie mayo, spread some on the bottom of each toasted bun. If using lettuce, place some on the bottom of each toasted bun. Top with the burgers, then top each burger with some carrot slaw. Add the top bun halves and serve immediately.