Peel and chop the onions, carrots and garlic, halve the pigeons, then pick and finely chop the parsley.
Heat the oil in a casserole dish over a medium heat, then sauté the onion, carrot and garlic until softened. Add the pigeon and brown for 3 to 5 minutes. Sprinkle the flour in and stir well.
Add the wine and stock, season generously, then increase the heat and bring to the boil. Lower the heat, stir in the parsley, then simmer with the lid on for 4 hours. Check on it now and again, adding an extra splash of water, if needed.
When the pigeon is nearly ready, use a fork to shred the meat off the bone – it should fall off easily. Serve with potatoes or crusty bread – be careful of the bones!