• 3/4c. grated or shredded Parmesan cheese
Preheat the oven to 375 degrees. Butter a 9-by-13-inch baking dish or casserole dish. Bring a large pot of salted water to a boil. Prepare an ice water bath. Add the beans to the boiling water and cook until tender, about 3 to 5 minutes. Drain the beans, then plunge them into the ice bath to stop the cooking. When beans are chilled, drain and set aside.
In a large, heavy-bottomed saucepan, melt 4 tablespoons butter over medium-high heat. Add shallots and cook, stirring occasionally, until translucent, about 3 minutes. Add the bell pepper and mushrooms and a pinch of salt and cook, stirring occasionally, until the vegetables have softened and the mushrooms have given up their liquid, about 5 minutes. Whisk in the flour and cook, stirring, for 1 minute more. Stir in the sherry, mixing well, then add the milk while whisking constantly. Bring to a simmer, stirring occasionally. Reduce the heat to medium-low and cook, stirring, until thickened, about 1 minute, then cook for 3 minutes longer.
Remove from the heat and whisk in the Boursin cheese, 1/2 teaspoon salt, pepper, lemon zest and tarragon. Taste and adjust seasoning with salt and pepper if needed. Add the reserved green beans and toss to combine. Transfer to the baking dish. (The recipe may be prepared up to this point 2 days ahead. Cover and refrigerate.)