Finely chop the shallot and parsley, mix together in a bowl along with the meat and all the other ingredients up to and including the pepper. Knead the mixture thoroughly until you have a compact mass.
With wet hands, shape the mixture into approx. 20 small burgers.
Slice the mushrooms, finely chop the shallot. Heat the clarified butter in a non-stick frying pan. Fry the burgers for approx. 3 mins. on each side, remove. Reduce the heat, wipe the cooking fat from the pan, add a little clarified butter if necessary. Sauté the mushrooms and shallot for approx. 5 mins.
Add the wine and reduce to half the amount. Thoroughly mix the cream, stock and cornflour, pour in and bring to the boil while stirring, cook for approx. 3 mins., season. Return the burgers to the pan, heat gently, cover and keep warm.
Peel the potatoes, cut into pieces along with the cauliflower. Cook the potatoes and cauliflower (uncovered) in boiling salted water for approx. 25 mins. until soft. Drain the water, allow the residual moisture to evaporate by swirling the pan on the switched-off hob.
Add the milk and butter, mash the potatoes and cauliflower with a potato masher or fork, season. Serve the mash with the burgers and sauce.