Cabbage: combine all ingredients and marinate in the refrigerator for at least 24 hours. Place marinated cabbage in a large pot, over low heat. Simmer for 1 1/2 hours, covered. Adjust seasoning. To reheat, saute cabbage over medium heat in 2 tablespoons of olive oil, just to heat and reserve.
Preheat oven to 450 degrees F.
Season loins liberally with kosher salt and pepper. Over medium high heat in whole butter, sear all sides. Place in oven for 7 to 10 minutes for rare to medium rare.
Sauce: Place jus in saucepan and bring to a simmer. Place quince in jus, simmer for 5 minutes, then add cold butter, whisking gently. Before serving, finish with thyme.
Place 1/4 of the cabbage in middle of plate. Place cake of semolina beside cabbage. Slice loin into 3 even slices and lay over the gratin. Drizzle quince and sauce around and on top of the caribou. Plate the remainder of the ingredients in the same way.
In a covered pot, cook the quince over low heat in the syrup, lemon, and water. When the quince is almost fork tender (20 minutes), remover cover and continue to cook for 10 minutes until quince is fork tender. Let quince cool in liquid. Keep refrigerated.
Bring milk to scald and add the butter, whisking quickly. While whisking, add semolina in a steady stream. Keep whisking until mixture thickens. Turn down heat and cook over low heat for 10 to 15 minutes. Remove from heat and whisk in the oka and yolks. Adjust seasonings.
Transfer to a casserole and sprinkle the gratin with the Parmesan and breadcrumbs. Refrigerate until ready to use. Quarter for serving.
Reheat in a 375 degree F oven for 12 to 15 minutes, gratin under a broiler to finish.
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