Slice the chicken into even, bite-size pieces and prepare all vegetables. Lightly bruise the lemongrass and measure sauces before cooking.
Heat 1 tbsp oil in a pan over medium heat. Add garlic and shallots and cook until fragrant and lightly softened.
Add green curry paste and stir for 1–2 minutes until aromatic and slightly darkened.
Slowly pour in coconut milk, stirring gently. Reduce heat to low to keep the sauce smooth.
Add chicken and simmer gently for 6–8 minutes, until just cooked through.
Add eggplant and cook for 3–4 minutes until tender.
Stir in bamboo shoots and snow peas. Simmer for another 2–3 minutes.
Season with fish sauce and sugar, tasting and adjusting for balance.
Turn off heat and stir in basil leaves and kaffir lime leaves.
Garnish with red chili, coriander, and lime wedges. Serve warm.