Preheat the oven to 350 degrees. Put the ricotta in a fine sieve and drain for 30 minutes. In a medium bowl, combine the drained ricotta, Parmesan, egg yolk, herbs, and lemon zest. Put the garlic cloves through a garlic press and add to the mixture. Combine well, adding the salt and pepper to taste.
Rinse the game hens and pat them dry. Season the cavities with salt and pepper and place a lemon quarter and an onion quarter in each cavity.
Loosen the skin on the breasts by sliding your fingers under the skin, being careful not to pierce it. Spoon the ricotta mixture under the skin (about 4 tablespoons of stuffing per bird). Truss the birds.
Place the birds, breast side up, in a shallow roasting pan. Pour the white wine into the pan. Bake for 1 hour, or until the juices run clear when the hen is pierced in the thickest part of the thigh. Remove from the oven, tent loosely with aluminum foil, and let rest 10 minutes. Discard the trussing string and serve with the pan juices spooned over the hens.