Rinse the jasmine rice under cold water until clear. Combine rice, 0.25 cup light coconut milk, water, and sea salt in a small saucepan; bring to a boil, then reduce heat to low, cover, and simmer for 15 minutes.
While rice cooks, slice the chicken breast into thin, bite-sized strips and season with black pepper.
Heat coconut oil in a large skillet or wok over medium-high heat. Add the green curry paste and sauté for 1 minute until fragrant and slightly darkened.
Add the chicken strips to the skillet and sauté for 3-4 minutes until the exterior is no longer pink.
Pour in the remaining 0.5 cup light coconut milk and chicken bone broth, stirring well to fully dissolve the curry paste into the liquid.
Add the sliced red bell peppers and sugar snap peas to the skillet. Simmer for 5-6 minutes until the vegetables are tender-crisp and the sauce has slightly thickened.
Stir in the fish sauce and coconut sugar, tasting to ensure a perfect balance of salty, sweet, and spicy flavors.
Remove from heat and stir in the fresh basil leaves. Fluff the coconut rice with a fork and serve the green curry over the rice in a shallow bowl.