Whisk ½ cup warm water, ⅓ cup fish sauce, and ⅓ cup granulated sugar together in a large bowl or airtight container until the sugar dissolves.
Remove the tough outer layers from 4 lemongrass stalks until you reach the tender center. Trim off the top and base. Crush the stalks with a meat mallet or heavy-bottomed pot to release the oils. Mince the stalks, or coarsely chop and then process the stalks in a mini food processor until finely chopped (about ½ cup).
Stir the lemongrass, 2 thinly sliced medium scallions, 2 tablespoons coarsely chopped garlic, and ½ teaspoon ground white pepper into the fish sauce mixture.
Pat 2 pounds boneless, skinless chicken thighs dry with paper towels. Trim off any excess fat, then cut each thigh in half crosswise. Add to the marinade and toss to combine, making sure the chicken is submerged. Cover and refrigerate for at least 12 and up to 24 hours.
Remove the chicken from the marinade and scrape off the lemongrass mixture as you best you can (some bits are OK).
Heat 2 tablespoons of the neutral oil in a 12-inch nonstick skillet over medium-high heat until shimmering but not smoking. Add half of the chicken in a single layer and cook until golden-brown, cooked through, and at least 165ºF on an instant-read thermometer, 3 to 4 minutes per side. Transfer to a serving plate.
Repeat adding the remaining 2 tablespoons neutral oil to the pan and cooking the remaining chicken.
Heat an outdoor grill to direct, medium-high heat (about 450°F to 500°F). Meanwhile, remove the chicken from the marinade and scrape off the lemongrass mixture as you best you can (some bits are OK).
Scrape the grill grates clean if needed. Place the chicken on the grill smooth-side down in a single layer, with space in between each piece. Cover and cook until dark grill marks appear on the bottom, 4 to 5 minutes. Flip the chicken, cover again, and cook until grill marks appear on the second side and the thickest part of the chicken registers at least 165°F on an instant-read thermometer, 3 to 5 minutes more. Transfer to a serving plate.
Let the chicken rest for 5 minutes. Cut into ½-inch slices. Serve with steamed rice and steamed broccoli if desired.
