Season the chicken breast evenly with sea salt and black pepper.
Heat the coconut oil in a large skillet or wok over medium-high heat until shimmering.
Add the chicken to the skillet and sear until golden brown and cooked through, approximately 5-6 minutes, then remove from the pan and set aside.
In the same skillet, add the green curry paste and sauté for 1 minute until the aroma is released.
Slowly whisk in the full-fat coconut milk and chicken broth, bringing the mixture to a gentle simmer.
Add the zucchini, red bell pepper, and bamboo shoots to the sauce and cook for 3-4 minutes until the vegetables are tender-crisp.
Stir in the fish sauce, coconut sugar, and lime juice to balance the savory, sweet, and acidic notes.
Return the cooked chicken to the skillet, tossing well to coat every piece in the green curry sauce.
Remove from heat, fold in the fresh Thai basil, and serve the curry immediately over the cooked jasmine rice.