In a large bowl, whisk together all of the ingredients except the Cornish hens. Put the hens in large resealable plastic bags and pour in the marinade. Seal the bags, pressing out the air, and turn to thoroughly coat the hens. Transfer the bagsto a small roasting pan or large rimmed baking sheet and refrigerate for at least 8 hours or overnight, turning the bags occasionally

Let the hens stand at room temperature for 30 minutes. Preheat the oven to 425° and line 2 large rimmed baking sheets with foil. Remove the hens from the marinade and transfer them to the baking sheets. Strain the marinade into a medium saucepan and bring to a boil, then simmer over moderate high heat for 5 minutes, stirring occasionally.

Roast the hens in the upper and lower thirds of the oven for 10 minutes, or until lightly browned. Reduce the oven temperature to 375°. Roast the hens for 50 minutes longer, basting with the reserved marinade every 15 minutes and shifting the pans from front to back and top to bottom halfway through roasting. The hens are done when the cavity juices run clear and an instant-read thermometer inserted in the inner thighs registers 160°.

Transfer the hens to a platter and let rest for 10 minutes before serving.