Cut away any brown spots from the beans, and trim off the stem ends (and the tail ends, if wilted); you should have about 10 ounces of trimmed beans. Combine the broth and brandy; set aside. Heat the butter and 1 tablespoon of the oil in a 10-inch straight-sided saute pan over medium-high heat. When the milk solids in the butter are just beginning to turn a nutty brown, add the beans and 1/4 teaspoon salt. Toss well with tongs and then arrange the beans in one layer. Cook without stirring until the bottoms are nicely browned, 3 to 4 minutes. Toss and turn over and cook for another 2 minutes to lightly brown another side. Transfer the beans to a plate with tongs.

Heat the remaining 2 tablespoons oil in the pan. Add the mushrooms and a pinch of salt and let cook without stirring until nicely browned on one side, 2 to 3 minutes. Add the ham and cook, stirring once or twice, until the ham and mushrooms are nicely browned, another 2 to 3 minutes. Return the beans to the pan, add the thyme, toss, and pour in the chicken broth and brandy. Immediately cover the pan and simmer until the liquid is almost completely reduced, 2 to 3 minutes. Uncover, add the cream and a few grinds of pepper, and cook for a few seconds longer, just to thicken the cream so that it coats the vegetables. Remove the pan from the heat. Serve right away as individual servings or pour and scrape the contents of the pan (except the thyme) onto a small platter and serve family style.