In a spice grinder, grind 2 tsp. juniper berries, the allspice, and peppercorns until coarsely ground. Add salt and whirl to mix.
Trim fat from steak. Rinse meat, pat dry, and rub all over with oil. Pat and rub spice mixture onto both sides.
In a 2-qt. pot, bring broth and remaining 2 tsp. juniper berries to a boil over high heat and boil until reduced by 3/ Add cream and 2 tbsp. gin and boil over medium-high heat until reduced by half.
Lay steak on an oiled cooking grate over a solid bed of very hot coals or highest gas heat (you can hold your hand 1 to 2 in. above grate for only 1 to 2 seconds); cover gas grill. Cook until firm when pressed on thin end but still quite pink inside (cut to check), 8 to 10 minutes; turn over halfway through. Meanwhile, reheat gin sauce over medium-low heat and, if more zip is desired, add 1 tbsp. gin.
Transfer steak to a carving board with a well (to catch juices). With a sharp knife, carve steak into thin, wide slices across the grain, holding the knife at a low angle to meat. Transfer steak to a warm platter; scrape drippings and juice from board into gin sauce. Serve meat slices with sauce.
Note: Nutritional analysis is per serving.