Position an oven rack in the center of the oven and preheat the oven to 375 degrees F.
Rinse the hens well under cool running water. Pat them dry with paper towels.
Melt the butter with the chopped fresh thyme in a small saucepan. In a small bowl, combine the juice of 4 lemons, honey, and soy sauce. Add the melted thyme butter and mix to combine. Reserve.
Heat a large cast iron pan on medium heat. Coat the bottom of the pan with olive oil.
Generously salt and pepper the hens and lay them skin-side down in the hot pan. Sear 4 minutes each side.
Pour 1/3 of the glaze on the bottom of a 9 by 13 baking dish. Transfer the hens, and their pan drippings, to the baking dish. Pour the remaining glaze over the hens and place in the oven for 30 minutes or until a thermometer reaches an internal temperature of 165 degrees F. Remove the dish from the oven and let them rest for about 5 minutes. Garnish with the sliced lemon and fresh thyme sprigs, and serve.
Cook's Note: to check the temperature, insert an instant read thermometer in the thickest part of the breast, avoiding any bones.
Notes*Cook's Note: Spatchcocking: Place the game hen breast side down on a cutting board. Using scissors or poultry shears, cut from the neck to the tailbone to remove the backbone. Make a small slit in the cartilage at the base of the breastbone to reveal the keel bone. Grab the bird with both hands on the ribs and open up like a book, facing down towards the cutting board. Remove the keel bone. Cut small slits in the skin of the bird behind the legs and tuck the drumsticks into them in order to hold them in place.