In a small skillet set over medium high heat, toast the raw rice (dry, no oil) until brown and fragrant, about 4 minutes. In a small food processor, or using a mortar and pestle, grind the toasted rice into a fine powder, set aside.
In a large skillet or braiser set over medium-high heat, sauté chicken until cooked through, drain over a colander, set aside.
Using the same large skillet, cook the shallots in the oil until tender, about 3 minutes. Add the chicken back into the pan. Add powdered toasted rice powder, brown sugar, lime juice, zest, salt, chili paste and fish sauce. Sauté for 3-5 minutes until all ingredients are fully incorporated and there is little to no crunch left from the rice powder. Remove from heat.
In a small bowl, mix all ingredients for the sauce.
Add the cilantro and mint to the chicken mixture.
Remove lettuce leaves from the stalk. Fill each lettuce cup/leaf with the larb mixture.
Serve drizzle with a little sauce.