FOR THE TOPPING: Pulse bread, butter, salt, and pepper in food processor until mixture resembles coarse crumbs, about ten 1-second pulses. Transfer to large bowl and toss with onions; set aside.

FOR THE VEGETABLES: In a large skillet over medium heat, melt 2 tablespoons butter. Add onion and garlic, sauté until it begins to soften, about 4 minutes. Add bell pepper and mushrooms, and cook until softened and most of the liquid has evaporated, about 8 minutes. Season with ½ teaspoon salt and ¼ teaspoon pepper. Set aside to cool.

FOR THE STRING BEANS: Prepare an ice bath: Fill a large bowl with ice and water; set aside. Bring a saucepan of water to a boil. Add beans, and cook until bright green and just tender, 4 to 5 minutes. Drain, and plunge into ice bath to stop cooking. When cooled, toss drained beans with mushroom mixture; set aside.

FOR THE SAUCE: Dissolve the cornstarch in 1/4-cup of the broth. Melt the remaining 4 tablespoons butter in a medium saucepan over medium-low heat. Add broth and heavy cream. When almost at a boil whisk the cornstarch and water together, then pour into the saucepan and bring to a simmer, about 30 seconds. Stir in cayenne, nutmeg, and the remaining ½ teaspoon salt and ¼ teaspoon pepper. Remove from heat, and let cool to room temperature. Pour over beans and vegetable mix, and toss to combine. Butter a 9-by-13-inch glass or ceramic baking pan. Spread the green-bean mixture over the bottom. Cover with foil, and refrigerate until just before serving.

Preheat oven to 350 degrees. Sprinkle topping and bake until golden brown, about 30 minutes.