Toast the walnuts and unpeeled garlic in a skillet over medium heat, stirring often, until the nuts are golden and fragrant, about 5 to 7 minutes. Transfer them to a bowl and, once the garlic is cool enough to handle, peel and roughly chop it.

Process the walnuts, garlic, cilantro, oil, lemon juice, scallion, salt, and pepper in a food processor for about 1 minute until smooth, scraping down the sides as needed. Taste the sauce and adjust with extra salt and pepper if desired.

Boil the green beans in 3 quarts of salted water until crisp-tender, about 4 minutes. Move the beans immediately to a large bowl of ice water for 2 minutes—this shocks the beans to stop the cooking and preserve their vibrant green color.

Drain the chilled beans thoroughly and transfer to a serving bowl. Toss with the cilantro sauce until evenly coated and serve at room temperature or chilled.