Melt the butter in a large heavy-based saucepan over a medium heat, then fry the whole pigeons for about 5 minutes, or until they have browned all over. Remove them and keep to one side.
Pour off most of the fat, leaving about 2 teaspoons in the pan, then add the garlic and fry for 30 seconds. Add the celery, leeks and potatoes and cook for 2-3 minutes, stirring frequently. Put a kettle of water on to boil.
Add the cayenne pepper and some salt to the vegetables, then add the pigeons, breast side down. Pour in 600 ml of boiling water, return to the boil and reduce the heat to low. Cover and simmer for 1 hour -1 hour 15 minutes until the pigeons are cooked through.
Meanwhile, heat a small heavy-based frying pan over a medium heat, add the cumin seeds, then turn off the heat and stir the seeds for 30 seconds -1 minute until they release their aroma. Crush them finely with a pestle and mortar or the back of a wooden spoon.
Remove the pigeons with a slotted spoon and purée the broth. When the pigeons are cool enough to handle, pull off and discard the skins. Cut off the meat using a small knife, then chop it into small pieces.
Put the meat and the puréed broth into a saucepan over a medium heat. Add the crushed cumin and milk and stir until the soup begins to bubble. Reduce the heat, stir in the fromage frais and cook for a further 1-2 minutes, then adjust the seasoning if necessary. Garnish with parsley or coriander and serve.
Variation: quail can be used instead of pigeon: just reduce the cooking time to 45-50 minutes.