Place the pork rack in the marinade and let it marinate it for 3 hours, refrigerated.
Remove the pork from the marinade. Season with salt and pepper. Divide the marinade into 2 portions. Reserve.
In a saute pan, over high heat, add the olive oil and 1 ounce of butter. Sear pork until golden. Transfer to a preheated 350-degree F. oven and roast for 20 minutes, basting with half of the reserved marinade every 5 minutes. Cook until meat thermometer inserted into the rack reads 150 to 160 degrees F. Allow to rest for 10 minutes before slicing into chops.
Meanwhile, in a saucepan, bring the remaining half marinade to a boil and reduce until thickened. Strain. Whisk in 4 ounces of butter. Season, to taste, with salt and pepper. Reserve.
In a saute pan, heat the remaining 1-ounce of olive oil. Saute the smoked bacon and garlic until golden. Add 4 ounces of butter and when melted, add the mustard greens. Season with salt and pepper. Deglaze with 6 ounces of chicken stock. Cover and cook for about 20 minutes, stirring occasionally. Reserve.
In another saute pan, heat the remaining 3 ounces of butter and melt. Add turnips and saute to golden brown. Add 6 ounces of chicken stock and 1 tablespoon of sugar. Braise until al dente. Season with salt and pepper. Reserve.
In the center of 4 plates, make a small mound with the mustard greens. Place pork chops against the greens. Place turnips around the greens and pork chops, and lightly ladle over the reserved pomegranate sauce. Serve immediately.
Prepare the pomegranate marinade. In a saute pan, heat the oil. Add the chilies and cook for 15 seconds. Transfer to a deep casserole, and add the garlic, ginger, green onions, pomegranate juice, rice wine vinegar, pepper, tamarind paste, brown sugar, coriander, and mushroom soy sauce.