Preheat the oven to 375° F.

Heat the oil in an ovenproof saucepan over medium-high heat. Add the sausage and cook, breaking it up with a spoon, until browned, about 5 minutes. Add the onions, carrots, and celery and cook, stirring, until softened, about 3 minutes. Add the garlic and orange zest and stir until fragrant, about 30 seconds. Add the rice and stir until it turns opaque, about 3 minutes. Stir in the raisins, almonds, parsley, thyme, and cinnamon.

Add the chicken stock and bring to a boil. Stir, cover the saucepan and transfer to the oven. Bake until the rice is tender and the liquid is absorbed, about 30 minutes. Remove the rice from the oven and spread it evenly on a large plate or baking pan to cool. Increase the oven temperature to 400° F.

Whisk the apricot jam, orange zest, sugar, and orange juice in a small saucepan over high heat. Cook until reduced by half, 8 to 10 minutes. Set aside to cool slightly.

Season the hens, inside and out, with the salt and pepper. Loosely stuff each hen with the cooled rice pilaf. Place the remaining pilaf in a small baking dish and cover with aluminum foil. Set aside.

Place the hens breast side up in a roasting pan. Brush some of the glaze on the hens. Roast, brushing every 15 minutes with more of the glaze, until the juices run clear and an instant-read thermometer inserted into the thickest part of the thigh registers 165° F, about 1 hour. Place the dish of rice pilaf in the oven to reheat during the last 10 minutes.

Serve the hens with the extra rice pilaf on the side.