Preheat oven to 375°F Line a rimmed baking sheet with parchment paper. Slice half the onion and place slices on baking sheet. Dice the rest of the onion for stuffing. Set aside.
Melt butter in skillet over medium heat. Add onion and ginger and cook until softened, about 2 minutes. Whisk in 3 tablespoons apricot jam and chicken stock. and bring to a boil. Remove from heat and add bread cubes. Stir and coat bread cubes. Let cool while preparing hens.
Wash and dry game hens. Season inside cavity with salt and pepper. Fill cavity with about 1/2 cup of the stuffing. Tie legs together with kitchen twine and use skewers to close cavity. Place breast side up on bed of onions. Season with salt and pepper.
GLAZE: Combine softened butter and 2 tablespoons apricot jam and spread over game hens.
Roast uncovered in a preheated oven for 60-70 minutes, or until internal temperature reaches 170°F Remove from oven, let rest about 10 minutes. To serve, cut each hen in half and serve with stuffing.
TIPS: Blueberry or Wildberry jam would be great with this as well.