Over high heat in an oven-proof skillet heat oil. Brown pork on all sides and transfer pan to 400F oven. Roast until cooked through -- about 20 minutes.
Melt butter in a large skillet over medium heat and add onions and shallots. Saute for 3 minutes and add wine and boil until liquid is reduced by half -- about five minutes. Add chicken broth and beef broth and boil until reduced to 6 Tbl -- over 20 minutes. Add cream and lime juice and reduce at a boil to 1 cup, about 7 minutes. Season with salt and pepper.
Slice meat and plate, smothering with sauce.