With the rack in the middle position, preheat the oven to 190 °C (375 °F).
In a bowl, combine 30 ml (2 tablespoons) of butter with the jam, mustard, and garlic. Season with pepper. Set aside.
With your fingers, gently lift the skin from the breast and thighs of the hens, without tearing it. Stuff with the butter and mustard mixture, covering evenly under the skin. Brush the hens with the remaining butter. With butcher's twine, tie the legs of the hens to give them their original shape, if desired. Season with salt and pepper.
Place the hens, breast side up, side by side in a baking dish. Pour the wine into the baking dish. Bake for about 1 hour or until a meat thermometer inserted into the thigh, without touching the bone, reads 82 °C (180 °F). Add wine, as and if needed, to always have about 250 ml (1 cup) at the bottom of the baking dish.
Serve half a hen per person with the cooking juices. Some good eaters will enjoy a whole hen. Serve with Stuffed Apples and a Spinach and Roasted Onion Salad.