Preheat the oven to 200 degrees C.
Peel the shallots and slice off the stalk end, leaving the root intact. Make incisions along the length of the shallot and then slice across the width to dice finely.
Peel and quarter the mushrooms.
Use a sharp knife to make small incisions in the skin of the duck breasts - do not cut too deeply or you will cut the meat. Season the meat side of the duck breast with salt. Fry the duck breast skin side down without adding grease to the pan. Cook for about 4 minutes over a medium to high heat. Before turning the duck over, drain away the grease that has been produced in the frying process and set aside to cool before disposing of it. Turn the duck breast over and cook for 3 more minutes then place on a baking tray and cook in the oven for a final 6 minutes.
Sweat the shallot in olive oil and a pinch of salt. Once the shallot is transparent add the mushroom and the sprigs of thyme. Cook for 6-8 minutes over a medium heat and season with salt and white truffle oil.
Serve the duck on a bed of mushrooms and garnish the plate with piment d`espelette.
«All varieties of mushrooms work well in this dish... chestnut, oyster, button etc. To prepare in advance, sear the duckbreast as described and then set aside until you are almost ready to eat, at which point you can finish cooking the duck breast in the oven.»