Place mustard in a medium mixing bowl, and slowly whisk in Herb Vinaigrette. Add shallots. Transfer to a small saucepan, and set aside.
In a 10-inch saucepan over high heat, bring court bouillon to a boil. Season both sides of the halibut with salt and pepper. Add halibut to the pot, and adjust the heat until the liquid simmers. Poach until a cake tester inserted into the center of the halibut meets little resistance and the cake tester, when left in the fish for 5 seconds, is just warm when touched to your lip, about 5 to 6 minutes. The halibut will be rare (thinner steaks will poach in less time). Transfer the steaks to a warm plate, and set aside.
Add the herbs to the vinaigrette, and warm over low heat. Remove the skin from the halibut, and place 1 steak in the center of each plate. Spoon the vinaigrette over and around the fish. Serve immediately.
In a small mixing bowl, whisk together mustard, salt, pepper, red wine vinegar, and sherry vinegar. Whisking constantly, slowly drizzle in olive oil, and then corn oil. Store, tightly covered, in the refrigerator for up to 1 week.
In a large saucepan over high heat, combine all ingredients with the water 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 for up to 2 months.
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