Bring 1/2 cup coconut milk to a boil in a heavy saucepan. Whisk in the curry paste and cook until fragrant, about 5 minutes. Add the chicken and cook until browned, about 5 minutes. Stir in the 2 cups coconut milk, fish sauce, sugar, vegetables, bamboo shoots, and basil; simmer until the chicken is cooked through, about 15 minutes. Pour the lime juice over the dish and remove from heat. Serve warm.