Heat a Dutch oven or heavy-bottomed pot over medium-high heat. Add the oil and saute the chicken until no longer pink, about 3 minutes. Season with salt and pepper. Remove the meat with a slotted spoon, reserving the fat and liquid in the pan.
Add in the water chestnuts, mushrooms, bell peppers and sliced scallions and saute for 10 minutes. Lower the heat to medium, add in the ginger and garlic and cook until fragrant, 15 to 20 seconds. Add the hoisin, soy sauce, mirin and cooked chicken and simmer for a couple more minutes. Taste and adjust the seasoning if necessary.
Thinly slice the reserved scallion tops. Scoop the chicken onto lettuce cups and garnish with the sliced scallions, chopped cashews, a bit of sriracha and a dash of fish sauce.