Add the chicken thighs to a mixing bowl and set aside.
Combine the lemongrass, shallot, garlic, lime juice, fish sauce, soy sauce, brown sugar, and 1 tablespoon olive oil in a blender and process until smooth.
Pour the blended marinade over the chicken, toss to coat, cover, and refrigerate for at least 30 minutes (or up to 8 hours).
About 5 minutes before cooking the chicken, rinse the jasmine rice under cool water until the water runs clear.
Place the rinsed rice in a saucepan with the coconut milk, water, granulated sugar, and kosher salt; bring to a boil, then reduce heat to low, cover, and simmer for 18–20 minutes.
Remove the rice from the heat and let it sit, covered, for 5 minutes, then fluff with a fork.
While the rice cooks, heat the remaining 1 tablespoon olive oil in a skillet or grill pan over medium heat.
Sear the marinated chicken thighs skin-side down until golden, about 6–7 minutes per side, and cook through.
Serve the cooked chicken over the coconut jasmine rice with fresh mint or cilantro and thinly sliced cucumber.