For the aïoli: Whisk the egg, lemon juice, lemon zest, garlic, mustard, salt, and peppers together in a small bowl until well blended. Starting slowly, drop by drop, whisk in ¼ C oil. After this is incorporated well you can add the rest of the oil in a thin stream whisking all the while. Taste and add more salt or lemon juice to taste. This needs to end up very thick so do not add too much lemon juice. Whisk in more oil in a thin stream if the sauce is not thick like commercial mayonnaise. (You can also use Best brand mayonnaise). Add 3 T of chiffonade basil (very finely shredded). Set aside.
For the halibut: Take one piece of halibut 5-6 oz per person, skin on, center cut to maintain the thickness of the whole filet. Place on heavy aluminum foil on a baking sheet. Score the fish from end to end diagonally every inch, cutting about halfway through the thickness of the fish on each diagonal cut. Turn the sides of the foil up around the edge of the fish, squeezing the corners of the foil to secure. Squeeze one-half lemon over the fish and salt and pepper to taste. Cover with the aioli. Sprinkle with paprika. Bake in a 450° oven for 15 minutes. Then check the center of the fish by separating with two forks to make sure the center is not pink or raw. Cook another 3-5 minutes if necessary. When done, separate the filet into serving size pieces and slide off the skin with a pie server and place on warm plates. Sprinkle with chopped basil and chopped parsley. Serve with cherry tomatoes sautéed in olive oil and butter with a pinch of sugar and salt, and Lebanese rice.