Grease a baking dish with butter and lay the fish inside. Add the button mushrooms, garlic, yellow onions and rosé. Cover with parchment paper and braise in the oven for 40 minutes. Transfer the fish to a platter and carefully pour the liquid through a strainer into a saucepan. Reduce the cooking liquid for 5 minutes. (Reserve the button mushrooms and yellow onions for a salad.)
Add the chanterelles, pearl onions, butter and the reduced cooking liquid to a sauté pan; cook for 5 minutes.
Gently remove the fish bones, and then cover the fish with the chanterelle sauce. Serve hot.