This general recipe will work with all small birds, from quail to snipe, doves, pigeons, partridges or teal ducks. You can very the vegetables, too, if you want. I like this over a simple plate of buttered wild rice.
Preheat your oven to 400F. Coat the vegetables and mushrooms in the oil, then salt well. Arrange in one layer in a pan and roast until nicely browned, about 45 minutes.
When they're done to your liking, peel the garlic, toss everything with a little Worcestershire sauce and serve with the woodcock.
WOODCOCK
While the vegetables are roasting, coat the birds with oil and salt well. Put the rest of the oil in a frying pan large enough to hold the birds and get it hot over medium-high heat. Remove the backbones from the birds and separate the legs from the breasts; keep the breasts on the bone as you see in the picture.
When it's hot, set the legs and breasts of the birds in the pan and start searing. Ideally there is enough oil in the pan to almost cover the legs, or at least halfway. Sear until golden brown, about 8 to 10 minutes total, flipping once or twice.
The way you cook the breasts is to keep them bone-side down most of the time. You spoon hot oil over the breasts to cook them while the legs are frying, and when the legs are almost ready, tip the breasts upside down to get contact with the hot oil directly. This will brown them. Only let this happen for about a minute per side -- since a breast won't sit flat, you will need to tip them to one side, then the other.
To finish, turn off the heat and add the butter. When it melts, spoon it all over the birds. This is for flavor. You've been using a neutral, high smoke-point oil, and this adds nice flavor. Serve with the vegetables and some wild rice.