1 tablespoon olive oil
1 tablespoon butter
3 large shallots, sliced thinly
8 ounces cremini or button mushrooms, sliced thinly
1/4 teaspoon salt
1 1/4 pounds green beans, stem ends trimmed
1/4 cup chicken, turkey, or vegetable broth
Heat the oil and butter in a large skillet over medium heat, swirling it around to coat the pan. When the butter is fully melted and has stopped foaming, add the shallots, mushrooms, and salt. Sauté until all of their liquid has evaporated from the mushrooms and they are beginning to brown, about 10 minutes.
Add the green beans to the pan and stir to evenly distribute the shallots and mushrooms. Pour the broth over the vegetables and cover the pan. Let cook, covered, until almost tender, about 10 minutes. Turn off the heat and let stand, still covered, for another 5 minutes.
Serve the green beans in a serving dish or shallow bowl, pouring all of the mushrooms and shallots over the top.