Combine the milk and the water in a large saucepan.
Add the coarse salt and the sweetbreads. Bring to the boil then reduce the heat to low and simmer for 15 minutes. Refresh under cold water.
Remove the fine membrane from the sweetbreads then devein and cut them into 4 cm cubes. Cut the kidney into similar size pieces and carefully devein.
Cook the carrots in a saucepan of boiling water fo 5 minutes, or until just tender. Drain.
Meanwhile, place the mushrooms in a saucepan and cover with hot water. Bring to the boil over a medium heat and cook for 5 minutes. Remove from the heat and let stand for 5 minutes to rehydrate.
Drain, reserving the cooking liquid.
Return the cooking liquid to the pan and cook over a medium-high heat until reduced by a quarter.
Melt half of the butter with the olive oil in a large frying pan over a medium-high heat.
Sauté the shallots, then add the mushrooms.
Stir in the carrots and sweetbreads, and finish with the pieces of kidney.
Brown everything, then flambé with the Cognac.
Add the reduced mushroom juice and season with salt and pepper. Use a slotted spoon to transfer the sweetbreads, kidneys and vegetables to a plate.
Whisk the remaining cold butter into the cooking juices and serve immediately.