1. Adjust oven rack to upper-middle position, place rimmed baking sheet on rack, and heat oven to 400°F. Using sharp knife, cut 1/4-inch-deep slits, spaced 1/2 inch apart, in crosshatch pattern on surface (non-gill side) of 8 mushrooms. Dice remaining 4 mushroom caps and reserved stems into 1/2-inch pieces; set aside (you should have about 6 cups).

2. Brush both sides of caps with 2 tablespoons oil and sprinkle evenly with 1 teaspoon salt. Carefully place caps, gill side up, on preheated baking sheet. Roast until mushrooms have released some of their juices and begin to brown around edges, 8 to 12 minutes. Flip caps over and continue to roast until liquid has completely evaporated and caps are golden brown, 8 to 12 minutes longer. Remove mushrooms from oven and heat broiler.

3. Pulse bread in food processor until coarsely ground, about sixteen 1-second pulses (you should have about 1 1/2 cups). Heat 1 tablespoon oil and 1 tablespoon butter in 12-inch skillet over medium heat until butter is melted. Add breadcrumbs and 1/4 teaspoon salt; cook, stirring frequently, until light golden brown, 5 to 8 minutes. Transfer crumbs to small bowl and wipe out skillet with paper towels.

4. Return now-empty skillet to medium-high heat, add 1 tablespoon oil, and heat until smoking. Add half of chopped mushrooms and cook without stirring for 2 minutes. Continue cooking, stirring occasionally, until lightly browned, 4 to 6 minutes longer. Transfer to medium bowl; repeat with remaining 1 tablespoon oil and remaining mushrooms.

5. Add remaining 1 tablespoon butter, prosciutto, and onions to skillet; cook, stirring occasionally, until onions are light brown, 5 to 6 minutes. Add garlic and cook until fragrant, about 30 seconds. Stir in sherry and cook until almost no liquid remains, 1 to 2 minutes. Reduce heat to low and stir in reserved cooked mushrooms, thyme, parsley, cheese, and cream. Continue cooking until cheese is melted and vegetables are well coated, 1 to 2 minutes. Remove pan from heat, stir in lemon juice, and season with salt and pepper to taste.

6. Flip caps, gill side up, and distribute filling evenly between mushroom caps; top each with 2 tablespoons of breadcrumb mixture. Broil mushrooms until crumbs are golden brown, 1 to 3 minutes. Serve immediately.

Serves 8 as a side dish or 4 as a main course