Heat a large nonstick skillet over high heat. Season the duck breasts with salt and pepper and sauté, skin side down, until the skin is well browned and fat is rendered. Turn over and cook until medium-rare, 5 to 6 minutes. Let rest for 4 to 5 minutes.
Heat the olive oil in a large skillet over medium heat. Add the chanterelle and oyster mushrooms, season with salt and pepper, and sauté until golden brown, about 3 minutes. Add the shallots, garlic, and tarragon and sauté until the shallots and garlic are soft, about 3 minutes. Set aside and keep warm.
Remove the skin and slice each breast.
To serve, arrange the slices of duck, overlapping in a fan shape on large plates, and spoon mushrooms around the duck.Servings: 4