Preheat oven to 350°.
Season the duck breasts generously with salt and pepper.
Sear duck breasts, skin side down, in an oven-proof pan over medium-high heat until nearly crisp. Carefully turn and place pan in the oven until meat is just firm or reads 130° on a meat thermometer. Remove to a carving board and loosely tent with foil.
In a large sauté pan, heat olive oil and butter over medium heat until foam subsides. Add porcini, shallots, celery, carrot, thyme and bay leaves and sauté until porcini begin to color. Deglaze the pan with sherry vinegar, and season with salt and pepper to taste.
Spoon a generous bed of porcini onto six warm plates, then fan sliced duck breast over porcini. Finish with sea salt and a sprig of thyme.