Peel the garlic, the shallot, clean the button mushrooms. Cut the shallot and mushrooms into small cubes (duxelle). Melt half the butter with 1 spoon of oil. Add the duxelle and brown. Salt and pepper. Reserve. Wash the Jerusalem artichokes, cut them into 4 or 6 depending on their size.

Wrap each turkey fillet in cling film, then tap them with a rolling pin (or the back of a pan) to flatten and tenderize the meat. In a salad bowl, mix the sausage meat with the mushroom duxelle. Distribute a tablespoon of stuffing in the middle of each fillet. Close, then using cling film, form spheres. Cut pieces of kitchen wire and place them crosswise in front of you. Place a turkey melon removed from the cling film, surround with breast (or bard) if you use it. Tie the strings to form the melon quarters. Reserve.

Return to the casserole dish where you browned the duxelle. Add the remaining butter and brown the stuffed turkey melons on all sides. Salt, pepper. Remove the melons from the casserole, replace with the Jerusalem artichoke quarters which you will brown in the remaining oil with the crushed garlic cloves. When they are nicely browned, put the turkey melons back in the casserole dish, pour in water and add thyme. Cover and simmer over low heat for 40 minutes. Watch the liquid which should reduce but not run out. If there is not enough, you can add more during cooking. Check the cooking of the Jerusalem artichokes by inserting the blade of a knife which should penetrate easily.