To Prepare the Oysters and Salad
In a large pot, place 4 cups of rice bran oil and heat on a medium flame until oil is consistently 320° F.
Combine lemon and orange juice in a bowl. Add dried seaweed and gently agitate with a spoon. Chill in refrigerator for 10 minutes. Drain well and discard juice. Seaweed should be soft and flavorful.
Quarter the avocado with a knife; carefully remove seed and skin. Season with salt and pepper to taste. Place each quarter on a separate plate and place in the refrigerator to chill.
Combine semolina and all-purpose flour in a bowl. Pour buttermilk in a second bowl. Place the shucked oysters in the buttermilk, then remove 1 at a time and gently coat in the flour mixture. Carefully add 1 oyster at a time to the hot frying oil and cook until golden brown, about 4 minutes. Remove from oil and rest on a paper towel. Season with salt and pepper.
To Prepare Aiolo
In blender, purée all ingredients except mayonnaise. Transfer to a bowl; whisk in mayonnaise. Season to taste with salt and black pepper. Chill until needed.
To finish the dish, remove the chilled plates with the avocado quarters from the refrigerator. Place 3 crispy oysters on top of each avocado. Scatter the seaweed salad between the oysters. Place a small amount of aioli on each oyster.
I suggest Cliff Lede Sauvignon Blanc as a great wine pairing with this dish.