Cook walnuts and garlic in 8-inch skillet over medium heat, stirring often, until toasted and fragrant, 5 to 7 minutes; transfer to bowl.
Let garlic cool slightly, then peel and roughly chop.
Process garlic, cilantro, oil, lemon juice, scallion, ½ teaspoon salt, and ¼ teaspoon pepper in food processor until smooth, about 1 minute, scraping down sides of bowl as needed; transfer to large bowl.
Bring 4 quarts water to boil in large pot over high heat. Meanwhile, fill large bowl halfway with ice and water. Add 1 tablespoon salt and green beans to boiling water and cook until crisp-tender, 3 to 5 minutes.
Drain green beans, transfer to ice water, and let sit until chilled, about 2 minutes.
Transfer green beans to bowl with cilantro sauce and gently toss.
Season with salt and pepper to taste. Serve.
