Dry the halibut cheeks with paper towel if they are wet. Lightly flour the cheeks, shaking off the excess flour. Season the cheeks with salt and pepper, if desired.

In a sauté pan large enough to have all the cheeks placed flat on the surface of the pan, add 3 tablespoons of unsalted butter to the warm pan. When butter melts add the cheeks. Sauté on one side until browned and then turn. This will take about 4 minutes per side.

While the cheeks are sautéeing, use a second pan to prepare the rice pilaf. Place one tablespoon of oil in a 1.5 quart pan.  Add finely diced onions and sweat until transparent. Add the rice and stir until all the kernels are coated with oil. Add the chicken stock and cover this pot. When the pot boils, turn down to a light simmer. When the stock is absorbed and the surface of the rice develops holes, remove pot from heat but leave the cover on. (About 15 minutes for the rice to finish from simmer point to being ready to serve.)

Place a tablespoon of butter in a third sauce pan. Sauté very lightly the shallots and garlic for two minutes. Add the lime juice, lemon juice and white wine. Turn up the heat and reduce this mixture until half the volume is evaporated. Add the heavy cream and again reduce until about half the volume. As the sauce simmers slowly, drop pieces of cold butter into the sauce whisking continually. When all the butter is absorbed in the sauce, it is ready to be served. This sauce can only be made 20 minutes ahead of serving, and it must be kept warm.

To serve, place pilaf in center of the plate. Top with browned Alaskan halibut cheeks, drizzle with lemon-lime butter and sprinkle with freshly chopped parsley.