Soak the glutinous rice in cold water for 1 hour, then drain well.
Rinse each chicken inside and out and pat dry. Loosely pack the cavity of each bird with the drained rice, 2 garlic cloves, and 3 jujubes — loosely, so the rice has room to swell.
Cross the legs and tie them with kitchen string, or tuck one leg through a slit cut in the other side of the cavity, so the stuffing stays in during cooking.
Set both stuffed chickens breast-up in a deep pot just large enough to hold them snugly. Add the ginseng, scallions, and water — it should cover the birds by about 2 cm / an inch.
Bring to a boil uncovered, skimming off the grey foam that rises in the first 5 minutes.
Cover, drop the heat to a gentle simmer, and cook for 60 to 75 minutes, until the leg bone wiggles loose with almost no resistance.
Lift each chicken carefully into a wide bowl — it will be soft enough to fall apart if you're rough with it — and ladle the broth and rice over the top.
Serve with a small dish of salt and pepper for dipping the meat, and scallions scattered over the broth.