For the beef and sauce, heat a little vegetable oil in a pan and add the shallots and garlic. Cook until lightly coloured.
Add the mushrooms and fry until cooked through.
Add the brandy and cook until the volume of liquid has reduced by half.
Add the stock and the thyme and, again, cook until the volume of liquid has reduced by half.
Add the cream and cook until the mixture has reduced to a sauce consistency.
Meanwhile, for the champ, place the potatoes in a pan of water and bring to the boil. Cook for 15-20 minutes, or until tender.
For the beef and sauce, put a large frying pan on a medium heat. Season the beef medallions, to taste, with salt and pepper. Rub with oil and fry on each side for at least two minutes, depending on how well done you enjoy your fillet. Keep warm until ready to serve.
For the champ, when the potatoes are cooked, drain well and mash until smooth.
Put the milk and spring onion into a small pan and bring to the boil. Simmer until the onions are cooked, then pass the mixture through a fine sieve. Stir the milk into the mashed potatoes and keep warm until ready to serve.
For the fricassée, bring a pan of water to the boil, add the green beans and simmer for four minutes. Prepare a bowl of ice cold water.
Remove the beans from the heat, drain and briefly place into the cold water. Drain again.
In a pan, lightly fry the shallot in a little oil and add the green beans. Season to taste with salt and freshly ground black pepper.
Serve the beef with the sauce, bean fricassee and champ.