Heat 4 tbsp oil in large skillet. Add garlic, ginger, eggplant, zucchini & green beans. Cook until almost tender, stirring often, about 10 minutes. Cover and cook until completely tender, about 3 minutes longer.
Transfer vegetables to bowl.
Add 1 tbsp oil, lime peel, and curry paste to same skillet; stir 15 seconds.
Add coconut milk; bring to boil, whisking until smooth.
Return vegetables to skillet; add onion and toss until sauce thickens enough to coat vegetables.
Serve over rice.