Persian or Indian near Hilton Kensington
That's rather closed to Mohsen. Given the fact you're staying at the Hilton Kensington I figure you can afford the taxi there which saves you a ride on the number 10 bus and any effort to hunt the place down opposite Home Base. It's probably one of the best if not the best Iranian restaurant in London.
You're also cab-able to Indian Zing though it's in Hammersmith and that place has been somewhat revolutionary on here for providing authentic Marathi cuisine. I believe Quilon is quite close by as well (high end Keralan with a very good veg thali.)
Finally, it's not Indian or Persian, but Chez Marcelle is in easy reach and if you go there for lunch on a Friday or Saturday you will have a life changing meal. Her starters are incredible and her specials of he day are usually excellent as well, but avoid the grilled meat items. Her fatoush is the best I've ever had by a long shot and my Lebanese friend declared it probably the best he'd ever had. This place is really worth your while and its either a quick ride on the District Line to Kensington Olympia followed by a quick walk or another short cab ride.