1. Combine 2 cups herbs, 1/4 cup scallions, ginger, and garlic in a food processor. Pulse to chop ingredients. Add 4 Tbsp each of oil and vinegar, and 1/4 cup water. Process until a coarse purée forms. Transfer herb sauce to bowl and stir in sesame seeds. Season to taste with salt and pepper. Herb sauce can also be made ahead. Cover and chill.
2. Heat 1 Tbsp oil in large heavy skillet over medium-high heat until oil just begins to smoke. Add remaining 1/4 cup scallions and wheat berries, farro or brown rice. Stir-fry until grains are golden brown and slightly crunchy, about 3 minutes. Season with salt and pepper. Divide grain of choice among bowls.
3. Return skillet to medium-high heat and add remaining 2 Tbsp 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 rice or grain bowls. Drizzle with herb sauce.