Heat oil in a heavy-based skillet over medium-high heat. Add curry paste along with the garlic, ginger, and lemongrass and cook for 2-3 minutes until the paste has mostly dried out.

Add the chicken broth and coconut milk, stirring to dissolve the paste. Add fish sauce, sugar, salt, and kaffir lime leaves, then bring to a simmer.

Add the chicken and lower heat to medium. Cook for 7 minutes, then add the eggplant and cook for another 5 minutes until soft.

Taste and adjust seasonings. Add the snow peas and cook for 2 minutes, then stir through the Thai basil and lime juice.

Serve over steamed jasmine rice.