In a medium saucepan, cover the brown rice with 2 inches of water and bring to a boil. Cover and cook over low heat until the rice is just tender, about 40 minutes. Drain and return the rice to the saucepan; keep covered.
Meanwhile, in a small saucepan, combine the quinoa with 2 cups of water and bring to a boil. Cover the saucepan and simmer over low heat until the quinoa is tender and all of the water has been absorbed, 20 minutes.
In a large skillet, heat 2 tablespoons of the oil. Add the onion and cook over moderate heat until translucent, about 4 minutes. Add the carrot and cook until starting to soften, about 3 minutes. Add the shiitake, cover and cook until tender, about 4 minutes. Add the zucchini, season with salt and cook, stirring a few times, until tender, about 3 minutes. Transfer to a bowl.
Add the remaining 2 tablespoons of oil to the skillet. Add the broccoli, cover and cook over moderate heat, stirring a few times, until deep green, 5 minutes. Add the kale, cover and cook, stirring a few times, until the broccoli and kale are just tender, 4 minutes. Season with salt. Stir in the other vegetables.
In a small bowl, whisk the tahini with the lemon juice, garlic, warm water and crushed red pepper. Season with salt.
Transfer the brown rice and quinoa to bowls. Top with the cooked vegetables, diced avocado and bean sprouts. Serve, passing the tahini sauce at the table.