Chop the vegetables into bite sized chunks. Broccoli, carrot and eggplant should be sliced thinner so they're not undercooked. In a wok, stir fry each batch of vegetables separately and reserve.
In a large pot, combine a few tablespoons of the solid part of the coconut milk with curry paste and cook for a few minutes. Add rest of sauce ingredients and cook 3 minutes. Add vegetables, stir well, and cook 5 minutes more.
Mix in lemon juice and thai basil leaves. Adjust seasoning and serve over rice.