To prepare the marinade, in a large ziplock bag, combine the wine, shallots, garlic, ginger, rosemary, and pepper. Seal the bag and shake it to blend the marinade. Place the steaks in the bag, seal it tightly, and massage the bag to thoroughly coat the meat with the marinade. Refrigerate for at least 4 hours, and up to 24 hours.
Meanwhile, to prepare the sauce, in a medium saucepan, combine the wine, allspice, rosemary, vinegar, pepper, brown sugar, and salt to taste and bring to a boil over medium heat. Reduce the heat to medium-low and simmer until the sauce is reduced to one-quarter of its original volume (roughly ⅔ cup), about 30 minutes. Stir in the demi-glace. (The sauce can be prepared to this point up to 1 day in advance and stored in the refrigerator.)
When ready to grill the steaks, prepare a high-heat grill.
While the grill heats, remove the steaks from the bag; reserve the marinade. Pat the steaks thoroughly dry with paper towels. Season with salt. Set aside.
If necessary, bring the sauce back to a simmer over medium heat. Add the reserved marinade and bring to a boil. Reduce the heat and simmer until reduced to a sauce consistency (the sauce should coat the back of a spoon), about 20 minutes. Taste and season with salt and/or brown sugar if necessary.
While the sauce simmers, grill the steaks for 4 to 5 minutes per side for medium-rare, or the desired doneness. Remove the steaks from the grill, transfer to a cooling rack, and let rest for about 6 minutes.
Meanwhile, strain the sauce and discard the solids.
Thinly slice the steaks against the grain. Serve with the sauce.