7 Tbsp. softened butter, divided
2 strips bacon, coarsely chopped
2 large garlic cloves, smashed
2 Tbsp. Dijon mustard
2 tsp. fresh thyme
1∕8 tsp. cayenne pepper (or more to taste)
2 1½-lb. Cornish game hens
Kosher salt and freshly ground black pepper, to taste
Olive oil, for searing
1 small shallot, minced
½ cup bourbon
Ύ cup chicken stock
2 Tbsp. whole-grain mustard
4 Tbsp. flour
Preheat the oven to 350 degrees. Line a baking sheet with foil and place a rack or broiler pan on top.
In the bowl of a food processor, pulse 3 tablespoons butter, the bacon, garlic, mustard, thyme and cayenne into a coarse paste.
Place the hens breast side-down on a work surface. Use sharp kitchen scissors to cut along each side of the backbone, then remove and discard backbone. Turn over and cut through breastbone to split in two. Using your fingers, carefully loosen the skin and spread the butter mixture under the skin. Season the hens with salt and pepper.
In a cast-iron skillet over medium-high heat, add just enough olive oil to coat the bottom. Add the hens skin side-down and sear until golden-brown, then flip and sear the other side, about 7 minutes each. Drain off all but 2 tablespoons fat in the skillet and set aside.
Transfer the hens skin side-up to the rack on the baking sheet and roast until the temperature in the thickest part of the thigh reaches 165 degrees, 20 to 25 minutes. Place on a serving platter and loosely cover with foil.
To make the pan sauce, place the skillet with the reserved fat over medium-high heat. Add the shallot and cook until softened, about 2 minutes. Add the bourbon and deglaze the pan, scraping up any browned bits. Add the stock and mustard, increase the heat to high and continue to simmer until the sauce is reduced by two-thirds, 5 to 8 minutes.
In a small bowl, mix the flour and the remaining 4 tablespoons butter to make a paste. Add a couple spoonfuls of the sauce to temper the mixture and stir. Reduce the heat to medium, then whisk in half the butter-flour mixture. Add more butter-flour mixture as needed to thicken the sauce.
Spoon the sauce over the hens and serve immediately.