Preheat the oven to 375°F.

Halve or thickly slice mushrooms that are larger than about 1 1/2 inches across; leave the rest whole.

Set 6 whole mushrooms aside.

Place remaining mushrooms on a large rimmed baking sheet and toss with oil and 1/2 teaspoon of the salt.

Roast until very soft and browned, about 35 minutes.

Meanwhile, skewer reserved mushrooms on 2 metal skewers.

Hold the ends of the skewers with oven mitts and place mushrooms over an open flame (such as a gas burner or outdoor grill on high setting) and cook, turning frequently, until charred all over, 3 to 4 minutes.

Remove mushrooms from the skewer and place on a cutting board. When cool enough to handle, coarsely chop.

Oil a 1 1/2-quart gratin dish or 8-inch-square baking dish.

In a large bowl, stir together half-and-half, half of the cheese, pepper, nutmeg and remaining 1/4 teaspoon salt.

Stir in roasted mushrooms and charred mushrooms.

Pour mixture into a gratin dish and press down gently with the back of a spoon to level.

Sprinkle with remaining cheese, parsley and bread crumbs.

Lower the oven temperature to 350°F; bake gratin until top is well-browned and edges are bubbling, about 40 minutes.

Cool 10 minutes before serving.