In a bowl, combine the lemongrass paste, soy sauce, fish sauce, brown sugar, and vegetable oil. Add the chicken thighs and marinate for at least 30 minutes, or up to 2 hours in the refrigerator for more flavor.
While the chicken is marinating, cook the rice noodles according to package instructions. Drain and rinse under cold water to stop the cooking process. Set aside.
Heat a grill pan or skillet over medium-high heat. Remove the chicken from the marinade and cook for about 5-7 minutes on each side, or until fully cooked and no longer pink in the center. Remove from heat and let rest for a few minutes before slicing.
To assemble the bowls, divide the cooked rice noodles among four bowls. Top each with mixed greens, shredded carrots, cucumber slices, and sliced chicken.
Garnish with fresh cilantro, green onions, and serve with lime wedges on the side for squeezing over the top.