6 tablespoons unsalted butter, plus more for dish
1 medium onion, diced
1 green bell pepper, seeded and diced
1 pound shiitake mushrooms, stems trimmed, quartered
2 teaspoons coarse salt
1/2 teaspoon freshly ground pepper
1 1/2 pounds green beans, trimmed and cut into 2-inch pieces
6 tablespoons all-purpose flour
2 cups milk
1 pinch cayenne pepper
1 pinch grated nutmeg
1 cup grated Parmesan cheese
1/4 cup breadcrumbs
1/4 cup canola oil
4 shallots, cut crosswise into 1/4-inch rings