Preheat oven to 400°. Clean hens by removing any excess fat or wayward feathers. Rinse inside and out, pat dry.
Finely chop rosemary, garlic, salt, and pepper until you have a nice uniform rub mixture. You can add more of any ingredient according to preference.
Sprinkle a little salt and pepper inside each hen and place 1/4 of the peeled onion inside. Rub the outside of each hen with the garlic and rosemary mixture. Place breast side up in a roasting pan. Generously pour over olive oil. There should be enough to make puddles on the bottom of the pan. Place in oven.
Roast until the breasts are starting to brown, then turn over. Be careful as the bottom side may stick and you want to avoid tearing the skin, if you can. Continue to roast until the bottom of the hens are brown. Turn again and pour over wine. Depending on the size of the pan, you may need more or less wine. DO NOT pour cold, white wine into a hot glass dish; Pyrex or not, it will shatter. It's OK if the oil is starting to brown, but you want to pour on the wine before the oil burns. Continue to roast until the hens are done and the wine, oil, and hen juices have made a creamy sauce. Total roasting time is about an hour.
Place the hens on the serving platter and strain some of the pan juice mixture over the top of the hens. You can any place extra in a small bowl or gravy boat to pass.