preheat oven to 375°F. heat olive oil in small skillet over medium high heat until very hot but not smoking. add 1/4 cup shallots and cook, stirring until golden brown and crisp. transfer with a slotted spoon to paper towels to drain. repeat with the remaining shallots cooking 1/4 cup at a time. reserve oil in pan.

Place green beans in steamer basket fitted over a pot of boiling water. Cover and steam until bright green and still crisp, about 3 minutes.

Heat 1 tbsp shallot oil in large deep nonstick skillet over medium high heat. Add mushrooms and cook, stirring occasionally, until mushroom liquid is evaporated and they begin to brown, about 12 minutes. Add garlic and thyme and cook, stirring, 1 minute. Transfer mixture to bowl.

Whisk together milk and flour until flour is dissolved. Add mixture to skillet and whisking constantly, bring to a simmer. Reduce heat to medium low, whisking occasionally, until tickened, 10 - 15 minutes. Remove the pan from the heat and stir in green beans, mushroom mixture, 1/3 cup parmesan, parsley, nutmeg,3/4 tsp salt and 1/2 tsp pepper.

Coat a 2 quart baking dish with cooking spray. Spoon green bean mixture into prepared dish and sprinkle top with shallots and remaining 2 tbsp parmesan. Bake until golden on top and bubbling, about 20 minutes.