Combine the dressing ingredients in a bowl and mix well with a fork. Set aside.
Heat 1 tablespoon of oil in a large skillet over medium-high heat. Add the chicken and saute until cooked through, stirring frequently and breaking up lumps, about 5-6 minutes. Remove from heat and season with salt and pepper to taste. Transfer to two serving plates, splitting equally.
In the same skillet, fry 2/3 of the thinly sliced shallots over medium-high heat. You may need to add a little bit of oil to the skillet if needed. Cook, stirring frequently, until golden brown and crispy, about 2-3 minutes. Remove from the pan and set aside.
Combine the remaining (uncooked) sliced shallots, lettuce, carrot, mint, cilantro and basil in a bowl and gently toss to mix well, adding the dressing a little at a time.
Transfer the salad to the serving plates. Sprinkle the peanuts on top if desired. Garnish with fresh cilantro and mint leaves, green onion and crispy fried shallots and serve.
Thai chilies can be sliced or minced, depending on your preference.