Prep the lemongrass: Trim off the root end and tough green tops. Peel off the tough outer layers until you reach the pale core. Smash the stalks with the side of a knife to release oils, then mince very finely.
Make the marinade: In a bowl, combine lemongrass, garlic, shallot, Thai chiles, fish sauce, soy sauce, brown sugar, oil, lime juice, lime zest, white pepper, and salt.
Stir until the sugar dissolves.
Marinate the chicken: Pat the chicken dry. Add it to the bowl, turning to coat well. Cover and refrigerate for at least 30 minutes, ideally 2–4 hours.
For deeper flavor, marinate overnight.
Bring to room temp: Take the chicken out of the fridge 15–20 minutes before cooking so it cooks evenly.
Stovetop method: Heat a large skillet or grill pan over medium-high. Add a film of oil. Cook the chicken 5–6 minutes per side, until browned and the internal temp reaches 165°F (74°C).
Avoid crowding the pan.
Grill method: Preheat the grill to medium-high and oil the grates. Grill 4–6 minutes per side, depending on thickness, until charred in spots and cooked through.
Rest and slice: Let the chicken rest 5 minutes. Slice against the grain or serve whole.
Spoon any pan juices over the top.
Serve: Plate with jasmine rice, a squeeze of lime, and a shower of cilantro. Add cucumbers for crunch and balance.