Make the Mediterranean garlic and spice marinade. Combine the garlic spice rub ingredients in food processor. Run the processor until you achieve a pasty spice mixture or rub.
Now to each of the hens, apply the marinade generously on the outside and in the cavities. Lift the skins and apply some of the marinade underneath (this is the key to flavor).
Heat a lightly-oiled cast iron grill or skillet. Turn the the heat to medium-high and brown each of the hens on all sides. Set the hens aside momentarily to cool.
Once the hens are cool enough to handle, stuff each hen's cavity with the chopped onions and celery. Now squeeze juice of one lime or lemon on the hens. Add all the used lime or lemon halves in with the onion and celery stuffing. Sprinkle each hen lightly with a dash of seasoned salt, if you like.
Place the hens in a large cast iron skillet or a roasting pan. Add two cups of good chicken broth from the side of the skillet.
Bake in the 425 degrees F heated-oven for 1 hour to 1 hour and 15 minutes or until the hen juices run clean, basting every 15 minutes with the broth. Remove from the oven and cover loosely with foil for 15 minutes before serving.
This recipe will serve 8 people (each having ½ of a hen).
Make ahead tips: Chop the vegetables a day in advance and store them separately in the fridge. You can also prepare the rub and apply it to the hens the night before you plan to roast them, and store the hens in the fridge in airtight containers.
Leftovers and storage: Once the Cornish hens have returned to room temperature, store them in airtight containers in the fridge for up to 3 days.