Artichokes à la Barigoule is a French preparation of spring artichokes braised in white wine and olive oil with onions, carrots, and aromatics, especially thyme. It is similar to carciofi alla romana, a similar Italian preparation of artichokes.
Note that artichokes à la barigoule does not contain Barigoule mushrooms. For a lengthy investigation of why this is so, see https://www.seriouseats.com/artichokes-a-la-barigoule-a-simple-french-dish-with-a-twisted-history