Preheat oven to 350 degrees F.

Heat the oil in a 2-quart saucepan over medium heat and add the sausage. Cook until the fat is rendered, about 4 to 5 minutes. Add the onions, carrots and celery and cook until the onions are translucent, about 3 minutes. Add the garlic and 1 teaspoon of the orange zest and sweat for about 30 seconds. Add the rice and cook stirring continuously for 3 minutes. Add the raisins, almonds, parsley, thyme, cinnamon, 1 teaspoon of salt, 1/2 teaspoon black pepper, the chicken broth and bring to a boil. Cover the pot and place it in the oven and cook for 30 minutes.

Remove the rice from the oven and increase the oven temperature to 375 degrees F. Place the rice on a sheet pan or a platter to cool.

Combine the apricot jam, orange juice and remaining zest in a small mixing bowl and whisk to blend. Place the glaze in a saucepan over high heat and bring to a boil. Allow glaze to cook until reduced by half. This will take about 8 to 10 minutes.

Season the hens with the remaining salt and pepper on the insides and out. Stuff each hen cavity with about 3/4 cup of the cooled rice and place in a roasting pan. Use a pastry brush to spread the glaze on the hens and place them in the oven.

Roast the game hens for 15 minutes, remove from the oven, and spread another layer of glaze over the hens. Return the hens to the oven and roast for an additional 15 minutes. Remove the hens from the oven, spread the glaze over the hens, and return to the oven.

Continue to cook for 30 more minutes, or until an instant read-thermometer inserted in the thigh registers 160 degrees F, and inserted into the rice registers 140 degrees F.

Serve the hens with any extra rice pilaf.