Combine warm water, fish sauce, and granulated sugar in a large bowl and stir until the sugar has completely dissolved.
Peel off the outer layers of lemongrass stalks to reveal the tender core. Cut off the ends and lightly crush the stalks to release their flavor. Finely chop the lemongrass using a knife or mini food processor.
Mix the chopped lemongrass, scallions, garlic, and white pepper into the fish sauce mixture.
Pat dry the chicken thighs, trim excess fat, and cut each thigh in half crosswise. Place the chicken into the marinade, making sure pieces are evenly coated and submerged. Cover and place in the refrigerator for 12 to 24 hours.
For pan-searing: Heat 2 tablespoons of neutral oil in a large nonstick skillet over medium-high heat. Remove chicken from the marinade, scraping off as much of the lemongrass mixture as possible but some bits can remain. Add half the chicken to the pan in a single layer. Cook each side for 3 to 4 minutes until the chicken is golden brown and reaches 165°F internally. Remove and set aside. Repeat with remaining oil and chicken.
For grilling: Preheat grill to medium-high heat (450°F to 500°F). Remove chicken from marinade, scraping off excess lemongrass mixture as best as you can. Oil and clean the grill grates if needed. Place chicken skin-side down spaced apart and cook for 4 to 5 minutes until marked. Flip and cover again, grilling another 3 to 5 minutes until chicken reaches 165°F internally. Remove from grill.
Allow chicken to rest for 5 minutes before slicing into 1/2-inch pieces. Serve with steamed white rice and broccoli if desired.