Step 1Combine salt and water in a large mixing bowl and stir to dissolve the salt. Add ice. Set the brine aside while you prepare the fish.
Step 2Cut the fish into 2 1/2-inch wide by 1-inch thick strips along the length of the fillet. (After brining, you'll cut the fish into cooking portions). Be sure to use the sharpest knife in the drawer for this and work slowly and carefully. Remove the blood line from the skin side of the fillets. Place the fillets in the brine and leave for 1 hour.
Step 3Remove the fish from the brine, dip briefly in salt-free ice water and dry it thoroughly with paper towels. Lay the fillets out flat on parchment-lined baking sheets and refrigerate, unwrapped, for a minimum of 4 hours.
Step 4Cut the fillets into 5- to 6-ounce portions, and prepare as you wish.
Step 5To grill the halibut, heat the grill over medium-high heat until hot and clean it well with a wire brush. Brush both sides of the fish with a very thin coating of mayonnaise and sprinkle with salt, if desired.
Step 6Just before putting the fish on the grill, wipe down the grate with an old rag that has been briefly dipped in cooking oil. Place the fish on the grill and, after a minute or so, turn the fillets at a 45-degree angle to mark them. After another minute, flip the fillets. Cook for 2 more minutes. The flesh should yield to gentle pressure when pressed (you can also use a cake tester to test the doneness of the fillet; when the fish is properly cooked, a cake tester will pass through with only gentle resistance).
Step 7Remove the fish to rest, preferably on a rack, for 5 minutes before serving.
Step 1Prepare the vinaigrette. Place the mustard, vinegar, sugar, salt, pepper and garlic in a mason jar. Place the lid on the jar and give it a good shake. This will dissolve the salt and the sugar. Remove the cap, add the oil, relace the cap and shake again. This will yield about 1 1/3 cups of creamy, well-emulsified vinaigrette, more than will be required for the recipe (the remainder can be stored tightly covered in the refrigerator for at least 1 week).
Step 2Blanch the green beans briefly in a large pot of rapidly boiling salted water and cook just until the color brightens, about 1 minute. Remove to a bowl of ice water to stop the cooking, then drain and pat dry.
Step 3Slice the tomatoes and arrange them on a large serving platter. Depending on the shape of the tomatoes, you may want to cut some into wedges and others may look better sliced. Season the tomatoes with Maldon salt and a few turns of freshly milled black pepper. Sprinkle the tomatoes with the chopped shallots and distribute half the green and opal basil, parsley and tarragon evenly over the tomatoes. This should be done one-half hour before you are ready to serve your guests.
Step 4Just before the fish is ready, shake the vinaigrette again to re-emulsify, and drizzle one-fourth of it over the tomatoes. Place the cooked and drained haricots vert in a mixing bowl and toss them with enough vinaigrette to coat them well and season with salt and pepper. Scatter a layer of beans over the tomatoes.
Step 5Place the grilled halibut on top of the tomatoes and the beans. Drizzle the halibut with more vinaigrette and scatter over the remainder of the dressed beans. Distribute the remaing herbs over it all. Pass the remaining vinaigrette at the table.