While many people might not be familiar with cornish game hens (aka young chickens), I actually grew up eating them. A lot of them. This particular dish is a riff on something my mother made that we referred to as "Chicken with Greens" because of the heavy dousing of oregano on top.
All in all, this dish is incredibly easy to make. I chose to use whole pearl onions and shallots instead of opting for fingerlings or other potatoes, but you can choose that route if you prefer. A less lazy cook than I would peel the onions, but I had just taken a kick-your-booty kind of class at the gym and wasn't sure how much longer I'd be able to stand up for. So, I simply rubbed them to remove any excess skin and placed them in the roasting pan as is (and they came out spectacularly).
I particularly love whole roasted onions and shallots (much like roasted garlic) because they completely break down and become ultra creamy and soft. You can also toss a garlic head in the pan as well if you'd like, just lop off the top and drizzle with some olive oil.
Preheat the oven to 400 degrees. Remove any excess skin from the birds, wash them, and then pat them dry.
Place the 2 birds and the onions in your roasting dish. Drizzle the oil over the birds and onions and coat evenly using your hands. Generously salt the birds, using your fingers to gently separate the skin from the breast meat to create a little pocket where you can place salt. Sprinkle a little salt on the onions and toss as well. Douse the oregano all over the birds and then place breast side up in the pan. Heavily sprinkle the top of each bird with more oregano.
Place a sprig of thyme and a shallot inside both birds (you can use a lemon or lemon wedge instead of a shallot if you wish). Place the third shallot in the pan alongside the onions (try to keep everything in an 1 layer so it cooks evenly.
Place in the oven until cooked through, about 1 hour. Discard the shallots inside the birds and serve with the remaining thyme.