Prepare the chicken brine 24 to 48 hours before you plan to brine. In a large bowl or 4-quart plastic container, combine 3 quarts of water with the salt and sugar.
Stir until most of the salt and sugar are dissolved. Add the remaining ingredients, and refrigerate for 24 to 48 hours before using.
To brine the game hens, rinse and place the hens in an 8-quart plastic or stainless steel container. Holding a strainer over the container, pour in enough chilled Chicken Brine to completely cover the game hens. Cover with a lid or plastic wrap and refrigerate for 3 hours.
To make the rub, combine the salt, espelette, pepper, coriander, and garlic in a small bowl and mix thoroughly. Reserve 1½ teaspoons for the Spicy Apricot Glaze and set aside.
In a separate small bowl, combine the butter and 3 teaspoons of the rub and mix until smooth.
Prepare the Spicy Apricot Glaze while the hens are brining. To make the Spicy Apricot Glaze, place all ingredients in a small bowl and stir until well
incorporated. Refrigerate in an airtight container until ready to use.
Once brined, remove and pat the game hens completely dry with paper towels.
Using poultry shears to spatchcock the hens, remove the backbones from the game hens and lay them out flat.
Rub the seasoned butter over and under the skin of the hens, sliding your fingers beneath the skin to gently separate it from the meat. Dust both sides of each game hen evenly with 1 tablespoon of rub.
Let the hens rest 1 hour at room temperature.
When you are ready to cook, heat the grill to 400º F, using the direct grilling method.
Place the game hens skin-side-down over the hot coals, close the grill lid, and cook 10 minutes.
Rotate the birds 90 degrees, and cook an additional 10 minutes. Flip the birds so they are skin-side-up. Cook an additional 10 minutes, or until a meat thermometer placed in the thickest part of the breast reads 170º F, and the dark meat is 175º to 180º F.
Transfer the game hens to a pan or clean work surface, and brush both sides with the Spicy Apricot Glaze.
Return them to the grill, skin-side-up, and cook 5 minutes to set the glaze.
Transfer the birds to a platter and let them rest 5 minutes before serving.