First, bring the water to a boil in a small saucepan. Stir in the rice, then cover and turn heat to low. Steam until rice is fluffy, about 20 to 25 minutes.
Next, prepare the sesame glaze. In a small saucepan, toast the sesame seeds over medium heat until golden, about 7 to 8 minutes. Give them a shake every few minutes to ensure they are evenly toasted.
In the meantime, whisk together the brown sugar and soy sauce in a small bowl until the sugar is dissolved. Then stir in the sesame oil, rice vinegar, chili oil, powdered ginger, and minced garlic.
Once the sesame seeds are toasted, add the sauce to the saucepan and stir to combine. Simmer until slightly thickened, lowering the heat if needed, about 8 to 12 minutes.
While the sesame glaze simmers, prepare the butter lettuce. Set aside any leaves that are too small or have large holes or rips and use for a different recipe. If there are any large leaves, gently rip them in half to make two smaller lettuce wraps.
Next, make the stir-fried chicken. Heat vegetable oil in a wok or large frying pan over medium-high heat, then add the chicken and stir-fry until partially cooked, about 2 to 3 minutes. Then, add the soy sauce and sesame oil and stir fry until the chicken is cooked through, another 2 to 3 minutes.
Finally, plate the lettuce wrap ingredients on a large platter for serving DIY-assembly style at the table. Transfer the sesame glaze to a small bowl and place it in the center of the platter. Then, arrange butter lettuce leaves, brown rice, chicken, scallions, and carrots on the platter.
To assemble each lettuce wrap: Cup a leaf of butter lettuce in your hand and spoon about 1 tablespoon of brown rice into it. Then, add some shredded carrots and scallions - just a few pieces of each. Finally, add 3 to 5 pieces of chicken and drizzle with sesame glaze.