Bring the vegetable stock, 4 1/2 cups of water, the allspice berries, black peppercorns and sea salt to a boil in a large pot, stirring to dissolve the salt. Remove the brine from the heat and set aside to cool. When the brine is cool place the Cornish hens into the brine and refrigerate for 2 to 3 hours.
Preheat oven to 180 degrees C. Remove the game hens from the brine and pat dry. Discard the brine.
Place the cut-up grapefruit, orange, lemon, lime, rosemary and thyme into a microwave-safe bowl and microwave on High for 2 minutes; with tongs, stuff the fruit and herbs into the cavities of the Cornish hens. Slather each hen with olive oil and sprinkle with salt and black pepper. Place the stuffed hens into a roasting dish, breast sides up.
Roast in the preheated oven until no longer pink at the bone and the juices run clear, about 1 hour and 45 minutes. For extra-crispy skin turn the oven heat up to 200 degrees C for the last 15 minutes of cooking. Allow the hens to rest for 10 minutes before serving.