Preheat the oven to 450 degrees.
In a large bowl, pour olive oil on the Cornish game hens. Using your hands, massage the oil all over the hens.
Season the inside of the game hens generously with salt. Stuff each with a piece of carrot, celery, and onion.
In a large roasting pan, spread out the sliced mushrooms, chopped carrots, celery, whole garlic, onions and rosemary. Lay the Game Hens on top of the herbs and vegetables.
Squeeze a little bit of lime on each hen. Then sprinkle the dried herbs on top of each (more salt and freshly ground pepper (to taste), garlic powder, lemon-pepper seasoning, Herbs de Provence).
Bake in the oven for 60 minutes, or until a meat thermometer reads 165 degrees F and the juices run clear.
Remove the hens from the oven and place on a tray. Loosely tent with foil and let rest before serving.
If your roasting pan is safe to cook on the stovetop, put it over two burners and turn the heat to medium-low. It's time to make the yummy gravy! If you do not have a stovetop friendly roasting pan, scoop out all the fat, juices, vegetables, and mushrooms and place it in a saucepan.
Add the chicken stock and bring to a boil, stirring constantly. Whisk in the cornstarch slurry and continue to stir until the gravy is thick to your liking. This may take 5-10 minutes.
Serve the Cornish Game Hens with your favorite sides. Ladle the stuffing on top.