Bring 1.25 cups water to a boil in a pot, add the white rice and 1/2 teaspoon salt, then reduce heat to low, cover, and simmer for 12-15 minutes until the water is absorbed and rice is tender. While the rice cooks, prepare all your vegetables: shred the gem lettuce, grate the carrots, slice the spring onions into rounds, cut the cucumber into thin batons, and mince the red chili. I like to keep my vegetables separate until assembly so they stay crisp and fresh—it makes a big difference in the final texture of the salad.
While the rice is cooking, pat the chicken breast dry and season both sides generously with the five-spice, 1/4 teaspoon salt, and 1/4 teaspoon black pepper. Heat 2 tablespoons of vegetable oil in a large pan over medium-high heat until shimmering, then add the chicken and sear for 3 minutes on each side until golden brown. Add 1.5 tablespoons of boiling water to the pan, reduce heat to medium, cover, and cook for 10-12 minutes until the chicken is cooked through. Once cooked, remove the chicken to a cutting board, let it rest for a few minutes, then shred it into bite-sized pieces.
While the chicken rests, prepare the sauce by combining the peanut butter with 1.5 tablespoons of boiling water in a small bowl, stirring until smooth and combined. Add the soy sauce, sesame oil, rice vinegar, minced chili, and sugar, then whisk everything together until you have a smooth, pourable sauce. Taste and adjust the balance of flavors—I find the sauce should be slightly spicy, tangy, and nutty all at once, so add a touch more lime juice if it needs brightness.
Fluff the cooked rice from Step 1 with a fork and transfer it to a large serving bowl. Add the shredded lettuce, grated carrots, sliced spring onions, and cucumber batons from Step 1 to the rice. Drizzle 2 tablespoons of olive oil and the juice from 1/4 fresh lime over the vegetables and rice, then toss everything together gently until combined and evenly coated.
Arrange the shredded chicken from Step 2 on top of the rice salad base. Pour the bang bang sauce from Step 3 generously over the chicken and salad, then sprinkle the sesame seeds evenly over the top. Toss everything together just before serving so all the components are well coated with the sauce and flavors are combined.