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.
•Beans can be trimmed 1 day ahead and kept chilled in a sealable plastic bag.Nuts can be lightly toasted 1 day ahead and kept chilled, covered.
