Step 1Heat the oven to 350 degrees. Wash the beets and, leaving them wet, wrap them individually in foil. Place in a roasting pan or on a baking sheet and bake until tender, about 1 1/2 hours. (To test, poke a thin-bladed knife through the foil.) Let the beets cool in the foil. (Alternatively, to cook in water, drop the beets into salted water to cover and bring to a boil. Cook over medium heat until tender, 45 minutes to 1 hour.)
Step 2When the beets are cool enough to handle, peel and cut into eighths.
Step 3Place the beets in the bowl of a food processor with the shallot, Worcestershire sauce, hot pepper sauce, vinegar, cornichons and capers. Pulse until the mixture is minced but not pureed. You may have to scrape the mixture down between pulses.
Step 4Spoon the mixture into a bowl and stir in the mayonnaise and parsley. Taste and adjust the seasonings; you may need to add salt and pepper and more vinegar, Worcestershire or hot sauce. (This dish keeps well up to 2 days. Refrigerate, keeping it well wrapped or in a covered container, and bring to room temperature before serving.) Garnish and serve with steamed fish.