Indeed, this is a slight misnomer. What or who is desi vs. South Asian? Recognizing that Indians from the subcontinent tend to have friction with the term "South Asian," it still encompasses the countries that share some cultural commonalities (like food, clothing, language, genetics).
That said, here are three *Indian *films to get started with:
-1. Dilwale Dulhania Le Jayange (1995)
-2. Sholay (1975)
-3. 3 Idiots (2009)
I don't expect any complete newbies to Indian film to hang around these parts, so feel free to add any more suggestions for those said noobs. After all, discussing Indian films is why this community exists. Posts may be in any appropriate language - know that your audience is predominantly English speaking.
OMG. Thank you.