How to Make It
Preheat oven to 450°F. Bring 4 quarts water to a boil in a large Dutch oven over medium-high. Add green beans, and cook until crisp-tender, about 4 to 5 minutes. Drain beans, and plunge into a large bowl filled with ice water to stop the cooking process. Drain beans, and dry thoroughly with paper towels.
Line a rimmed baking sheet with aluminum foil; lightly coat with cooking spray. Toss together mushrooms, 3 tablespoons oil, 1/8 teaspoon salt, and 1/8 teaspoon pepper in a bowl; arrange evenly on prepared baking sheet. Roast at 450°F until mushrooms are deep brown and crisped, 12 to 15 minutes, stirring halfway through. Transfer mushrooms to a bowl; set baking sheet aside.
Whisk together lemon juice, remaining 1/4 cup oil, remaining 5/8 teaspoon salt, and remaining 3/8 teaspoon pepper in a large bowl until blended. Add beans; toss to coat. Gather beans into 10 bundles of about 20 beans each. Place 1 bundle at the end of 1 prosciutto piece; roll up lengthwise. Repeat with remaining 9 bundles and remaining 9 prosciutto pieces.
Arrange assembled bundles, seam side down, on reserved baking sheet. Bake at 450°F until beans are warmed and prosciutto begins to brown, 5 to 7 minutes. Transfer green bean bundles to a platter; sprinkle with roasted mushrooms.