6 tablespoons unsalted butter2 teaspoons crumbled dried thyme2 teaspoons dried sage2 teaspoons freshly grated lime zest1 teaspoon kosher salt4 1½-pound Cornish hens, rinsed and patted dry1 pound shallots, trimmed and peeled1½ tablespoons extra virgin olive oil1 cup chicken broth½ cup red wine1 tablespoon cornstarch, dissolved in 2 tablespoons red wine1/3 cup dried cherries1 tablespoon balsamic vinegarIn a small bowl, mix together 4 tablespoons of the butter with the sage, thyme, zest and salt until well blended. Loosen the skin covering the breast meat on each hen by slipping your fingers under the skin and sliding them between the skin and the meat.Divide the butter mixture among the hens, inserting it under the skin of each hen and smoothing it evenly by rubbing the outside of the skin. Season the hens with a little additional kosher salt and pepper.Preheat the oven to 425 degrees. In a roasting pan large enough to hold the Cornish game hens, toss the shallots with the oil, and salt and pepper to taste, and roast them in the middle of the oven, stirring occasionally, for 25 to 30 minutes, or until they are golden.Arrange hens, breast side up, on top of the shallots. Roast in the middle of the oven for 25 minutes. Reduce oven temperature to 350 degrees.Continue roasting until juices run clear when thigh is pierced at the thickest part, or until a meat thermometer inserted in the fleshy part of the thigh registers 175 degrees. Transfer the hens with the shallots to a platter and allow to stand while making sauce.Add the broth with the half-cup of wine to the roasting pan and simmer on the stovetop for 5 minutes, scraping up the brown bits from the bottom of the pan.Strain the mixture through a fine sieve set over a small saucepan. Whisk the cornstarch mixture and add it to the saucepan with the cherries and vinegar; add salt and pepper to taste. Simmer the sauce, whisking, for 5 minutes.Serve the hens with sauce.Makes 4 servings.