haha, yet another cultural thing I was completely obvious of before steemit. Here in the 'South' (aka backwoods NC) then this is just pan frying. Deep frying is dropping something into a massive deep vat of oil and letting it swim until it's crispy. Sauteeing to me is more what you are describing as pan frying.

Great idea with the parmigiana oysters & eggplant....may have to give that a try one day.