Combine half the oil, 2 tablespoons of the soy sauce, the fish sauce, garlic and ginger in a bowl. Add the chicken and toss to coat. Cover and refrigerate for at least 3 hours.
Add the rice to a saucepan of boiling water and cook for 10 minutes, until almost tender. Add the snow peas for the last 2 minutes. Drain in a sieve and rinse with cold water.
Combine the lime zest and juice with the remaining oil and soy sauce in a large bowl. Add the rice and snow peas, coriander, Chinese cabbage, cucumber and spring onions and toss together.
Preheat the grill (broiler). Lift the chicken strips out of the marinade, reserving the marinade, and thread onto metal skewers (or onto soaked bamboo skewers if you want to leave the chicken on them for serving). Grill (broil) for 8-10 minutes, turning to brown the chicken evenly, until cooked through.
Meanwhile, to make the dressing, put the onion, peanut butter, chili, coconut milk, sugar and reserved marinade in a small saucepan. Bring to a boil, then reduce the heat and gently cook, stirring, for 5 minutes. If the dressing is too thick, add 2-3 tablespoons water.
Spread the salad over a large platter. Remove the chicken form the skewers and arrange on top of the salad. Drizzle the chicken with the dressing and serve warm or at cool room temperature.
Per serving: 653 calories, 39 g protein, 28 g fat (8 g saturated fat), 62 g carbohydrate (7 g sugars), 4 g fibre, 1196 mg sodium