Mix all the ingredients of the marinade well and set aside. Preheat the broiler and grill the chicken breasts till they start to get golden on the outside and are about half cooked through. Slice the chicken into strips as thin as possible. Blanch the squid in a large pot of boiling water for 1-2 minutes, until it turns completely white. Drain and rinse with cold water. Combine squid, chicken and marinade and lit it sit for 1 hour at room temperature or 3 hours in the fridge.
Soak the bean thread noodles in warm water until they are soft, about 10 minutes. Drain immediately and rinse with cold water. Set aside.
Heat the chicken broth in a skillet, add the bean threads, and cook, stirring, until they are translucent, about 1-2 minutes. With a slotted spoon, transfer the marinated squid and chicken to the noodles in the pan and stir them into the noodles.
Line a platter with half the Bibb lettuce leaves. Tear the remaining leaves and mix them with the romaine lettuce. Layer the torn lettuce, red onion, bean sprouts, and cucumber over the Bibb lettuce. Heap the noodle mixture in the center of the vegetables and sprinkle dressing all over. Alternate wedges of tomato and lime around the edge of the mound and garnish the platter with the mint or basil.
From the Dinner Co-op