Place the cooked green beans in a serving dish and keep them warm until the toppings are ready.
For the shallots, break up the rounds into individual rings before you cook them, so they will crisp up more as they fry. Heat the olive oil over medium-high in a medium skillet. Add the shallots and cook, stirring frequently, until the rings get brown and start to look crispy. Do not let them burn, but let them get nicely browned. Drain on paper towels and sprinkle with a little salt.
For the sauce, heat the butter over medium-high in a large skillet. Add the mushrooms, garlic, white pepper, and salt, and cook, stirring frequently, until the mushrooms are softened. Increase the heat to high and add the sherry. Cook until the sherry has mostly cooked off, and there is only a little liquid around the mushrooms. Add the cream and cook, stirring frequently, until the sauce has reduced enough to easily coat a spoon.
Pour the mushrooms and sauce over the green beans, and top with the fried shallots right before serving.
