Step 1In a mortar and pestle, smash the garlic and salt into a paste. In a large bowl, whisk the egg yolk until smooth. Whisk in the lemon juice. Slowly drizzle in the canola oil, whisking to make a thin mayonnaise. Whisk in the garlic-salt paste and the olive oil. Just before serving, mix in the tarragon.
Step 1Slice the potatoes across, not lengthwise, about one-quarter-inch thick. Put them in a pot with the garlic, onion and salt and add water to cover. Bring to a boil over high heat, then reduce the heat and simmer until tender, 8 to 10 minutes.
Step 2Pour off the water carefully and add ice water to stop the cooking. Drain, then pat the slices dry with a paper towel and lay flat.
Step 3Clarify the butter by melting over low heat until it separates. Skim the foam, leaving 2 tablespoons clarified butter.
Step 4Just before serving, heat the clarified butter in a large skillet and add the potatoes. Cook on both sides, turning gently, to heat through, about 5 minutes. Season with the salt and pepper and sprinkle with parsley.
Step 1Heat the olive oil until almost smoking in a heavy iron skillet. Add the fish and cook until the bottom is golden brown, about 2 minutes. Turn over the fish and cook for 1 minute for medium-rare. Squeeze a couple of drops of lemon juice on each filet.
Step 2To serve, overlap four to five potato slices to make a circle in the center of each plate. Place one filet on top of the potatoes, and serve the aioli in a ramekin on the side.