Preheat the oven to 425 degrees.
Combine the juniper berries, Szechuan and black peppercorns, and thyme in a resealable plastic bag and crush underneath a heavy cast-iron skillet. Rub all over the rack of venison. Place in a roasting pan and roast for 25 minutes. Remove to a cutting board to rest.
Meanwhile, skim the fat from the pan, place the pan on the stovetop, and turn the heat to high. Add the pomegranate juice and bring to a boil, scraping the bits from the sides of the pan until the liquid is reduced to a thick syrup. Add salt to taste.
Carve the rack into 4 chops and arrange among 4 dinner plates. Drizzle the pomegranate sauce over each chop and garnish with the parsley.