For 3 people, which is what fits into a large Casserole:
4 Potatoes sliced
9 or 10 shallots peeled and cut in half (2 Onions roughly chopped would do as well)
3 Carrots cut into chunks
1 Bulb of Fennel sliced
2 stalks of Celery cut into chunks
3 Large Mushrooms quartered (or a whole bunch of small mushrroms would do to)
Handful of Thyme
2 cloves garlic sliced
Several knobs of butter
Some stock (mine was left over pork gravy padded out with vegetable stock, but chicken stock would probably do better).
Heat the oven to 200C. Heat a knob of butter in a big casserole. When it's melted, brown the pigeons on all sides. Take the pigeons out and put them on a plate, preferably somewhere warm.
Heat another knob of butter in the casserole. Add the shallots and garlic. Cook them until they're about to go brown, then throw in the celery, carrot and fennel. Again, cook until they're about to soften, then turn off the heat, stir in the thyme, some salt and pepper and the mushrooms.
Layer the potato slices on top of the vegetables. Pour in the stock; it should not quite get over the top of the potatoes. Put the pigeons on top. Try and get the lid on; you may need to shift things around a bit. Put it in the oven for 30 minutes, then take the lid off and cook for a final ten minutes. Serve. It really wants some bread to mop up the juice, which is a little thin, but delicious.
 Sorry, didn't really pay attention to how much I used
 I actually forogot about the mushrooms, so they had to sit on top with the pigeons