Preheat broiler. Melt 2 tablespoons of the butter in a skillet over medium-high. Add onion, bell pepper, celery, scallions, and garlic. Cook, stirring, until vegetables soften, 5 to 7 minutes. Add oysters and mushrooms. Bring to a simmer, and cook, stirring often, 5 minutes. Set aside.
Melt 1 tablespoon of the butter in a small saucepan over medium. Whisk in flour, and cook, whisking constantly, until smooth, 30 seconds to 1 minute. Add cream, and cook, whisking constantly, until very thick and beginning to bubble. Add Parmesan, and cook, whisking constantly, until cheese is melted. Remove from heat.
Using a fine wire-mesh strainer, strain oyster mixture; discard liquid. Add oyster mixture to cheese sauce; stir until fully incorporated. Stir in salt, pepper, and nutmeg. Spread mixture in a lightly greased (with cooking spray) 11- x 7-inch baking dish. Melt remaining 2 tablespoons of butter; toss breadcrumbs with melted butter. Sprinkle breadcrumbs over oyster mixture.
Broil on middle rack of oven until breadcrumbs are deep golden brown and mixture is bubbly, 4 to 5 minutes.