For the Aioli:
1 egg yolk
1 T lemon juice
1/4 t lemon zest
1 small garlic clove, finely chopped or grated
1 t dry mustard mixed into a paste with 1 T warm water, 1/2 t sea salt, 1/4 t cayenne pepper, 1/4 t ground black pepper
1/2 c + 3 T light olive oil or other light oil such as canola or grapeseed
Fresh basil, finely shredded

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. Once 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 1 C. Best brand mayonnaise). Fold in 3 T basil and set aside.

For the Halibut:
Halibut, skin on, center cut to maintain thickness of whole filet (5-6 oz per person)
Lemon
Salt and pepper to taste
Paprika to taste

Place on heavy aluminum foil on a baking sheet. Score the fish from end to end diagonally every inch, cutting about half way 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 remaining basil and chopped parsley, if desired. 

Serve with cherry tomatoes sautéed in olive oil and butter with a pinch of sugar and salt, and Lebanese rice.