Simple dish Idly has been in controversy regarding the origin.
Idly in literature
‘iddalige’, first mentioned in a Kannada work Vaddaradhane of Sivakotyacharya in 920 AD. The Sanskrit Manasollasa of 1130 AD has ‘iddarika’. Tamil apparently only first mentions ‘itali’ in the 17th century.
Gujarati origin
Gujarat have IDADA which is steamed dhokla made from same ingredients as Idly.Namely Urad dhaal and Rice which are fermented overnight and next day steamed.Gujarathis claim Idaly is a dish which came to south from Gujarat during 10/12th century AD.when lot of silk weavers from saurashtra came to south via Maharashtra.The dukkia is first mentioned in AD 1068 in Gujurathi Jain literature, and dhokla appears in AD 1520 in the Varanaka Samuchaya. Besan flour is fermented overnight with curd, and steamed in slabs which are then cut into pieces and dressed with fresh coriander leaves, fried mustard seeds and coconut shreds. A coarser version is khaman and both are popular breakfast and snack foods in Gujurat. But we have to note that Gujart was ruled by chalukyas and Rastrakutas for many centuries before that and Idada may be from iddalige. Since we dont find references to that before that.
Indonesia origin
Acharya notes:the use of rice grits along with urad dhal,the long fermentation of the mix, and the steaming of the batter to fluffiness. Only after 1250 AD are there references to what seem to be idlis as we know them. Achaya’s contention is that this absence from the historical record could mean that idlis are an imported concept — perhaps from Indonesia which has a long tradition of fermented products, like tempeh (fermented soy cakes), kecap (from where we get ketchup) or something called kedli, which Achaya says, is like an idli. This is plausible enough given the many links between Southeast Asia and South India, through rulers and traders. Acharyra also adds many legendary stories ,but there is no basis for them. When we look forward to literary evidences in Indian literature , Acharya does not give any in Indonesia.
Heuan tsang says no steaming vessels south india in seventh century.But steaming vessels are not required for steaming dishes , steam can be produced using cloth over the vessel, still this method is used in south India.
Karnataka origin
Vaddaradhane by Shivakoti Acarya ( Rashtrakoota times)of the 10th century names Iddalige ( Idli ), Holige (Poli) and Savige ( Vermicelli). The 12th century encyclopedia Manasollaasa of Somashekhara Ballala III (Kalyani Chalukya) is a veritable treasure house of recipes and cooking styles. Lets not forget that these were empires with catholic tastes and wide trading hinterlands.
Tulu and kannada dishes
Many old words appearing in the Vaddaradhane,but extint now in modern Kannada, are existing still in Tulu even now.Like "muttukadi","baikam"(Baikampadi) etc. Hale(Old) Kannada and Tulu shared many words. They also should have shared rice dishes like iddli(<-iddalige). We are handicapped by the absence of Tulu texts dating back to 10th C. AD or older ones.Compare this with the numerous leaf based steam cooked Tulu rice dishes similar to iddli in technology.However it is difficult to trace the antiquity of these leaf-wraped precursors of iddlis. Since,leafy vessels are more primitive designs than the more modern iddli cooking vessels, Tulu disheslike moode,gunda,kotte etc., can be said to be actual ancestors of the modern iddlis.
The first appearance of the term in the literature need not mean the origin of the dish around that time, so the origin of this delicious dish has to be karnataka. So Idli is defintely a Karnataka dish.