Preheat the oven to 375° F

Heat the butter in a medium skillet over medium heat. Add the onions and cook for 1 to 2 minutes, then add the mushrooms and cook for an additional 5 minutes or until the onions are translucent.

Add the flour and milk stirring constantly, cook about 2 minutes, season with salt and pepper. Add parsley and thyme, remove from the heat.

Rub the inside of 6 small ramekins with butter and then add mushroom mixture into each ramekin. Add 1 egg to each, season with salt and pepper. Add 1 tablespoon heavy cream and 1 tablespoon parmigiano-reggiano cheese. Place the ramekins in a baking dish and bake about 8 to 10 minutes. Serve immediately.