Bring the court bouillon to a boil in a flameproof roasting pan. Season the skate with salt and pepper. Add the skate to the roasting pan and poach until a knife will go easily into the crease between the skate ribs, about 1 minute.
In a bowl, toss the mesclun with 3 tablespoons of the vinaigrette. Arrange in a tall mound in the center of 2 dinner plates.
As soon as the skate is cooked, separate it into thin strips, cutting through the natural creases in the fish. Drape the strips over the salad in a circle, as if making a teepee.
Drizzle the skate with the remaining 2 tablespoons of vinaigrette. Scatter the coriander and the tomato over all. Serve immediately.
Combine all ingredients in a large saucepan and bring to a boil. Boil for 10 minutes. Strain through a fine-mesh sieve. Store, tightly covered, in the refrigerator for up to 3 days, or in the freezer up to 2 months.
In a mixing bowl, whisk together the mustard, salt, pepper and vinegars. Whisking constantly, very slowly drizzle in the olive oil and then the corn oil. Store, tightly covered, in the refrigerator for up to 1 week.
Courtesy of Le Bernardin Cookbook