For the sesame aioli: Soak the hijiki in warm water for 5 minutes. Drain, chop and set aside.
Heat the olive oil in a small skillet over medium heat. Add the garlic, ginger, jalapeno, and shallots to the oil and saute until they soften, about 45 seconds. Make sure you don't brown the ingredients. Next, add the soy sauce, mirin and rice wine vinegar. Turn the heat up to a boil, and reduce by half, about 1 minute. Remove from the heat.
In a bowl, add the mayonnaise, hijiki and the reduced soy sauce mixture. Stir until combined. Then, slowly add the sesame oil while stirring. Yield: 1 1/2 cups.
For the oysters: Heat the lap cheong in a saute pan over medium heat until it is slightly rendered, about 1 minute. Remove the lap cheong from the pan and dice.
Next, add the olive oil, garlic and shallots to the saute pan and cook over medium heat until they're nice and toasty, about 1 minute. Make sure you don't brown the garlic and shallots. Then add the spinach and cook until it is lightly wilted. Remove the spinach from the heat and allow to cool. Finish with salt and pepper to taste.
Preheat a grill to medium heat.
Wash, scrub and shuck your oysters. Remove the oysters from the shells and fill the shells with sauteed spinach. Place the oysters on top of the spinach. Then top each of the oysters with more sauteed spinach, some sesame aioli and lap cheong.
Put the oysters on the grill, close the lid and within 5 minutes they will be ready to eat.
To plate, place some salad on a platter, such as mizuna, a Chinese lettuce. Then, set the 12 oysters on top of the salad and garnish with lemon wedges.