Melt 2 tablespoons butter in a pan over medium-high heat. Add onion, bell pepper,celery, and mushrooms. Cook, stirring frequently until vegetables are soft, about 5 to 7 minutes.
Add garlic and cook 1 more minute.
Add drained oysters and cook, stirring frequently, until oysters are about halfway cooked. Pour entire contents of pan (oysters and vegetables) through a fine-meshed sieve and discard all liquid. Transfer everything in the sieve to a greased 11x7-inch baking pan. Season lightly with salt and pepper.
In a small saucepan, melt 1 tablespoon butter. Add flour and cook and stir for 1 minute.
Gradually whisk in cream and cook until it begins to simmer and thicken.
Add Parmesan cheese, whisk until melted, and remove from heat. Stir in salt, pepper, and nutmeg. Pour over the oysters.
Melt remaining 2 tablespoons butter. Toss with Panko crumbs and green onions. Sprinkle on top of casserole.
Place under broiler and broil until Panko crumbs are golden brown and mixture is bubbly.