2 1/2 pounds green beans, trimmed
5 tablespoons unsalted butter
1/3 cup shallot, finely chopped (about 2 medium)
3 tablespoons packed light brown sugar
1 teaspoon kosher salt, or to taste
1/2 teaspoon freshly ground black pepper, or to taste
Heat oven to 350°F with rack in middle. Spread out pecans on a rimmed sheet pan and bake in oven until pale golden on inside, about 6 to 8 minutes. Cool and coarsely chop. Have ready a colander submerged in a large bowl of ice water. Cook beans in a 6- to 8-quart pot of well-salted boiling water, uncovered, until just tender, 5 to 8 minutes. Using a large slotted spoon and/or tongs, transfer beans to colander in ice water to stop cooking, then drain well and dry on towels. Heat butter in a 12- to 14-inch deep heavy skillet (preferably straight-sided) over moderately high heat until foam subsides, then add shallot and cook, stirring until pale golden, 2 to 3 minutes. Reduce heat to medium and stir in sugar until almost dissolved, then cook pecans, stirring, 1 minute. Add green beans, kosher salt, and pepper, and sauté beans, turning them with tongs, until heated through, 2 to 4 minutes. Transfer to a platter and serve.