Fill a large mixing bowl with ice cubes and water and set aside. Fill a 6- or 7-quart pot two-thirds full of well-salted water. Bring the water to a boil and boil the beans uncovered until tender to the bite, 4 to 6 minutes. Drain, transfer to the bowl of ice water, and let sit until cooled, about 2 minutes. Drain and pat dry.

Put the pancetta in a 12-inch nonstick skillet and cook over medium-low heat until crisp and browned, 10 to 12 minutes. Transfer to a paper-towel-lined plate and coarsely crumble. Remove the pan from the heat and let it cool slightly.

Add 2 tablespoons of the olive oil to the pan and return it to medium-high heat. Add the mushrooms, shallots, and 1/4 teaspoon salt and cook, stirring frequently, until both are nicely browned and shrunken, about 5 minutes. Add the sage and cook, stirring, until fragrant, about 30 seconds. Take the pan off the heat and add the vinegar, mustard, and the remaining 1 tablespoon oil. Stir to combine.

Return the pan to medium heat, add the green beans and toss to combine and heat through, 2 to 3 minutes. Season to taste with salt. Transfer to a warm serving platter and garnish with the pancetta.

The beans can be boiled and refrigerated up to 6 hours ahead. The remaining ingredients can also be prepped up to 6 hours ahead and held in the refrigerator. An hour before finishing, remove the beans from the refrigerator to come to room temperature.