Slice the chicken breast into thin, bite-sized strips and season 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 strips to the pan and sear until golden brown on the outside, approximately 3-4 minutes, then remove the chicken and set it aside on a plate.
Reduce the heat to medium and add the green curry paste to the remaining oil, stirring constantly for 1 minute until highly fragrant.
Slowly pour in the full-fat coconut milk and chicken bone broth, whisking steadily to fully incorporate the curry paste into the liquid.
Stir in the fish sauce and coconut aminos, then bring the mixture to a gentle, steady simmer.
Add the sliced red bell pepper, sugar snap peas, and drained bamboo shoots to the simmering sauce.
Return the seared chicken and any accumulated juices back into the skillet.
Continue to simmer for 5-7 minutes until the vegetables are tender-crisp and the chicken is cooked through.
Remove the skillet from the heat and stir in the fresh lime juice and Thai basil leaves, allowing the basil to just wilt into the sauce before serving.