Place the chicken thighs in a large bowl and set aside.
Add the lemongrass, shallot, garlic, lime juice, fish sauce, soy sauce, brown sugar, and 1 tablespoon olive oil to a blender and blend until smooth to make the marinade.
Pour the 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 cold water until the water runs clear.
Combine the rinsed rice, coconut milk, water, granulated sugar, and kosher salt in a medium saucepan and bring to a boil.
Once boiling, reduce heat to low, cover, and simmer gently for 18–20 minutes until the liquid is absorbed; then remove from heat and let sit, covered, for 5 minutes. 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 chicken, skin-side down, 6–7 minutes per side until golden and cooked through.
Serve the chicken over the coconut jasmine rice topped with fresh mint or cilantro and thinly sliced cucumber.
