The filling can be made up to 2 days ahead and refrigerated. Rewarm the filling before stuffing the mushrooms. We do not recommend roasting the mushrooms in advance, as they become leathery once rewarmed. When shopping, choose dense mushrooms with a cupped shape. Blue cheese can be substituted for the goat cheese. This recipe can be easily halved.
1. Adjust oven rack to upper-middle position, place rimmed baking sheet on rack, and heat oven to 400 degrees. Using sharp knife, cut 1/4-inch slits, spaced 1/2 inch apart, in crosshatch pattern on surface (non-gill side) of 8 mushrooms. Dice remaining 2 mushroom caps and reserved stems into 1/2-inch pieces; set aside (you should have about 3 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. Meanwhile, place spinach and water in large microwave-safe bowl. Cover bowl with large dinner plate (plate should completely cover bowl and not rest on spinach). Microwave on high power until spinach is wilted and decreased in volume by half, 3 to 4 minutes. Using potholders, remove bowl from microwave and keep covered 1 minute. Carefully remove plate and transfer spinach to colander set in sink. Using back of rubber spatula, gently press spinach against colander to release excess liquid. Transfer spinach to cutting board and roughly chop. Return spinach to colander and press again. Set aside.
4. Pulse bread in food processor until coarsely ground, about 16 one-second pulses (you should have about 11/2 cups). Heat 1 tablespoon oil and 1 tablespoon butter in 12-inch skillet over medium heat until butter is melted. Add bread crumbs 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.
5. Return now-empty skillet to medium-high heat, add remaining tablespoon oil, and heat until smoking. Add 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.
6. Add remaining tablespoon butter 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, spinach, thyme, goat cheese, cream, and walnuts. 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.
7. Flip caps, gill-side up, and distribute filling evenly among mushroom caps; top each with 2 tablespoons bread crumb mixture. Broil mushrooms until crumbs are golden brown, 1 to 3 minutes. Serve immediately.
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Molly Birnbaum is the executive editor of Cook's Science at America's Test Kitchen. She previously served as managing editor of Modern Farmer magazine and project editor of The New York Times best-selling Cook's Illustrated cookbook, The Science of Good Cooking, and their most recent, Cook's Science. Her writing has appeared in The New York Times, ARTnews magazine, NPR's Cognoscenti, O, The Oprah Magazine and Atlas Obscura. She is the author of Season to Taste.