Preheat oven to 400 degrees F.

Heat oil in heavy large ovenproof skillet over high eat. Add pork and brown on all sides, turning frequently. Transfer skillet with pork to oven and roast pork until cooked through, about 20 to 30 minutes.

Meanwhile, melt butter in heavy large skillet over medium heat. Add onion and shallot and sauté 3 minutes. Add wine and boil until liquid is reduced by half, stirring occasionally, about 5 minutes. Add both stocks and boil until liquid is reduced to 6 tablespoons, stirring frequently, about 13 minutes. Add whipping cream and boil until sauce is reduced to 1 cup, stirring frequently, about 7 minutes. Mix in fresh lime juice. Season sauce to taste with salt and pepper.

Cut pork diagonally into 1/4-inch-thick slices. Spoon sauce onto plates. Fan pork atop sauce and serve.