Place the rosemary, bay leaves, and lemon slices along the bottom of a medium saucepan. Arrange the tuna on top, and pour the oil over to cover completely. Sprinkle with the salt and pepper. Cook over low heat for about 8 to 10 minutes, until the first bubble appears in the oil. (It should still be cool enough to be able to dip your finger in it.)
Immediately remove the pan from the heat, flip each piece of fish over, and cover the pan with a lid. Allow the tuna to sit in the warm oil for about 5 to 10 minutes, until it's cooked all the way through. Remove the tuna and refrigerate. Strain the oil and reserve for the Remoulade, chilling it for at least 30 minutes, or until cooled to room temperature.
Prepare Remoulade, as described in the recipe below.
Place the tuna in a medium bowl and, using your fingers, flake it into large chunks. Add 3/4 cup of the Remoulade and mix to combine. Season with salt, pepper, and lemon juice, to taste. If you like, add the remaining Remoulade.
Adjust the oven rack to the upper position, and preheat the boiler.
Toast the bread, and the rub 1 side of each slice with the garlic clove. Place on a baking sheet, garlic side up.
Pile the tuna unevenly over the bread. Crumble the cheese and scatter it unevenly over the center, leaving a 1-inch border of tuna around the edge. Heat under the broiler for about 30 seconds, until the cheese is melted. Squeeze a few drops of lemon juice over and sprinkle with chives.
In the bowl of an electric mixer or in a medium stainless steel bowl, whisk the egg yolk, salt, and mustard by hand. Slowly drizzle in the oil, drop by drop, whisking constantly. As the mixture begins to thicken, add a teaspoon each of the lemon juice and water.
Once you've added almost half of the oil, place the bowl in the mixer fitted with the whisk attachment, and mix on medium speed, or continue to whisk in the oil by hand. Pour the oil in a slow, steady trickle, scraping down the sides of the bowl as necessary. As the mixture thickens, add a little more of the lemon juice and water, and continue whisking until the remaining oil is completely incorporated and the sauce is thickened.
Stir in the red onion, capers, cornichons, tarragon, and parsley. Season with lemon juice and salt, to taste.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.