Preheat oven to 375 degrees F (190 degrees C). Grease a 9 inch glass pie dish.
In a medium bowl whisk together eggs, cream, salt, pepper and nutmeg. Set aside.
In a large skillet melt the butter over medium heat. Add the onions and garlic and cook until softened, about 5 minutes. Add the mushrooms and cook until they are tender and all of the liquid has evaporated, about 8 minutes.
Sprinkle in the flour and stir to combine. Cook for an additional 2 minutes.
Remove from heat and stir in 1/2 cup of the Gruyere cheese.
Spread mushroom mixture into prepared pie dish. Pour egg mixture over top. Sprinkle remaining 1/4 cup cheese over top of quiche.
Bake in preheated oven for 25 to 30 minutes or until set in center.