Whisk first 5 ingredients in bowl to blend for marinade. Place hens in plastic bag. Add 1 cup marinade; seal bag. Let hens marinate 1 hour or refrigerate overnight. Reserve remaining marinade.
Preheat oven to 400°F Place rack on large rimmed baking sheet. Arrange hens on rack; drizzle with marinade from bag. Roast hens until cooked through, basting occasionally with reserved marinade, about 1 hour.
Transfer hens to platter. Scrape juices into saucepan; add broth and any remaining marinade. Bring sauce to boil. Season with salt and pepper; spoon over hens.