To prepare the marmalade, bring the onions and stock to a simmer in a heavy-bottomed saucepan over medium-high heat. Reduce the heat to low, cover, and let gently simmer for 1 hour, stirring occasionally.
Meanwhile, put the cream in a small heavy-bottomed saucepan and bring to a simmer over medium heat. Reduce the heat to low and simmer for 30 minutes or until the cream reduces by half.
Uncover the onions, add the salt and pepper, and increase the heat to medium. Cook the onions, stirring occasionally, for about 10 minutes or until the liquid begins to get syrupy. The onions should be very slightly browned. Stir in the reduced cream and simmer for about 20 minutes or until the mixture is a little thicker than heavy cream.
Add the vinegar, stir to combine well, and simmer for 1 to 2 minutes to meld the flavors. Keep warm while cooking the fish. (Cooled and then tightly covered, the marmalade will keep in the refrigerator for 2 to 3 days.)
Preheat the oven to 400 degrees F.
Rinse the flounder and pat dry. In a shallow plate, combine the flour, salt, and pepper. Dredge both sides of the flounder in the seasoned flour, shaking to remove the excess.
Heat the oil and butter in a large skillet over medium-high heat until the butter begins to sizzle. One at a time, carefully lay the flounder in the skillet, white-skin side down. After 2 minutes, sneak a peak at the bottom side to make sure it is browning without burning, but don't be timid--a nice nutty brown is good. Carefully turn the flounder with a spatula and cook about 2 minutes or until browned. Transfer the fish to a baking sheet large enough to hold them all in a single layer.
Roast the flounder in the top third of the preheated oven for 6 to 8 minutes, depending on their size. Look closely: the inside of the fish should be just flaky and opaque. It is important not to overcook them. While the fish are roasting, warm the marmalade to a simmer. Place the fish on warm serving plates, top with the warm sauce, and serve immediately.
Recipe from Louis Osteen's Charleston Cuisine by Louis Osteen. Copyright 1999 by Louis Osteen. Reprinted by permission of Algonquin Books of Chapel Hill, a division of Workman Publishing.