How to Make It
Combine all of the sauce ingredients except the dissolved cornstarch in a small bowl; then stir in the dissolved cornstarch.
Slice the chicken across the grain into 1/4 -inch strips. Transfer to a bowl and toss with the cornstarch.
Heat a large wok. Add the cashews and toss over high heat until they begin to brown, about 15 seconds; transfer the nuts to a medium bowl.
Heat the peanut oil and 1 teaspoon of the sesame oil in the wok. Add the chicken, spreading the strips in a single layer, and stir-fry over high heat until golden and just cooked through, about 3 minutes. Add the chicken to the cashews in the bowl.
Heat the remaining 1 1/2 teaspoons of sesame oil and the chili oil in the wok. Add the bell peppers and stir-fry over high heat for 30 seconds. Add the snow peas and stir-fry until all the vegetables are crisp-tender, about 2 minutes. Return the chicken and nuts to the wok. Stir the sauce, then add it to the wok and stir-fry until the sauce is clear, about 2 minutes. Spread the lettuce on a platter, spoon the stir-fry on top and serve at once.