Sauté the Garlic and Ginger: Heat the coconut oil in a large skillet over medium heat. Add the garlic and ginger and sauté for about 1 minute, until fragrant. Be careful not to let the garlic brown.
Bloom the Red Curry Paste: Add the Thai red curry paste. Use a spatula to break it up and cook with the garlic and ginger for about 2 minutes.
Make the Coconut Curry Sauce: Pour in the coconut milk and ¼ cup water. Add the brown sugar, fish sauce, and makrut lime leaves. Stir well and bring to a gentle simmer.
Add the Chicken: Spread the sliced chicken into an even layer, making sure it is fully submerged in the sauce. Reduce the heat to low, cover, and simmer for about 8 minutes, or until the chicken is almost fully cooked.
Adjust the Seasoning: Taste the curry sauce and add more fish sauce or salt to your desired saltiness. If the sauce has reduced too much, add a splash of water.
Add the Vegetables: Add the red bell pepper, snow peas, and bamboo shoots. Simmer for about 2 minutes, until the vegetables are tender but still slightly crisp.
Finish With Thai Basil: Stir in the Thai basil and turn off the heat. Serve immediately with hot steamed jasmine rice.