Step 1In a medium saucepan, combine the water, wine, onion, carrot, fennel, garlic, peppercorns, mustard seed, red pepper flakes, bay leaf and one-half teaspoon salt and bring to boil. Reduce the heat to a quick simmer and cook until the liquid is reduced by half, about 25 minutes. Taste and add more salt if necessary; the liquid should be very flavorful. Cool to room temperature.
Step 2Trim the fins from the fillets and cut each diagonally in half crosswise. When the liquid has cooled, place the fish in a broad, deep skillet and pour the cool liquid over.
Step 3Slowly heat just until the liquid trembles a few times, about 15 minutes. The fish should be firm, and there may be some white collagen breaking on the surface. If not, cook a little longer over very low heat. Remove from heat and cool in the liquid.
Step 4When cool enough to handle, carefully remove the fillets from the liquid and gently peel away the skin.
Step 5Arrange the fillets in a single layer in a glass or porcelain dish, discarding the vegetables. Stir the lemon juice into the liquid, then strain it over the top of the fish and seal tightly with plastic wrap. Refrigerate until ready to serve. It will keep several days in the refrigerator as long as the fish is completely covered by the liquid.
Step 1Combine the pickling liquid, capers, chives and lemon juice to make a dressing.
Step 2Place a handful of mixed greens on each plate and add a mackerel fillet. Drizzle each fillet with several tablespoons of dressing and serve.