Season chicken with salt and pepper. Heat oil in a large skillet or braiser over medium-high heat. Add chicken and brown on both sides, about 3 minutes per side. Remove from the pan and set aside.
Add the curry paste, garlic, ginger, and lemon grass paste and cook, stirring for 2 minutes or until fragrant. Add the chicken broth, coconut milk, sea moss, and coconut sugar. Bring to a simmer. Return the chicken to the pan, cover the pan, lower the heat, and simmer for 20 minutes, stirring occasionally. Add the eggplant, snow peas, lime zest and juice, and basil. Cover and simmer for another 5 minutes or until the chicken reaches an internal temperature of 165°F.
Serve over rice and garnish with more basil and chopped peanuts.