Mix all the ingredients for the ahi tuna patties in a large bowl. Divide into 6 equal portions and press into patties. Preheat the griddle (or a skillet) to medium heat. Once it's very hot, brush the surface with sesame oil and place the patties on the hot surface. Sear the patties for 3 minutes per side, so the interior ahi chunks are still a little pink. Flip carefully. These patties are fragile.
Then immediately grill or sear the pineapple slices for 1-2 minutes per side.
Whisk together the ingredients for the hoisin mustard. Then spread the mustard on the buns and stack the burgers with lettuce, ahi tuna patties, grilled pineapple, and fresh avocado slices. Serve warm!