3 cups mixed tender herbs (such as basil, Thai basil, mint, cilantro, tarragon, and celery leaves), divided
1/2 cup thinly sliced scallions, divided
1 1/2" piece peeled ginger, sliced
1 garlic clove
7 tablespoons vegetable oil, divided
2 tablespoons unseasoned rice vinegar
2 tablespoons sesame seeds
Kosher salt and freshly ground black pepper
2 cups cooked, cooled wheat berries, farro, or brown rice
4 cups chopped mixed summer vegetables (such as bell peppers, eggplant, chiles, zucchini, summer squash, carrots, celery, radishes, and cherry tomatoes)
Combine 2 cups herbs, 1/4 cup scallions, ginger, and garlic in a mini-processor. Pulse to chop ingredients. Add 4 tablespoons oil, vinegar, and 1/4 cup water and process until a coarse purée forms. Transfer herb sauce to a bowl and stir in sesame seeds. Season to taste with salt and pepper. DO AHEAD: Herb sauce can be made 2 hours ahead. Cover and chill. Heat 1 tablespoon oil in large heavy skillet over medium-high heat until oil just begins to smoke. Add remaining 1/4 cup scallions and wheat berries. Stir-fry until wheat berries are golden brown and slightly crunchy, about 3 minutes. Season with salt and pepper. Divide wheat berries among bowls. Return skillet to medium-high heat and add remaining 2 tablespoons oil. Add vegetables, season with salt and pepper, and stir-fry until brightly colored and crisp-tender, about 4 minutes. Add remaining 1 cup herbs and toss to combine. Divide vegetables over wheat berries. Drizzle with herb sauce.