Thanks pevergreen, Vasziljevics
I knew it had been a while since I'd played EU3, but that's actually a rule I've never encountered before.
And to pay it forward...
gll25:
To become Mughalistan, a country must not be Persia or the Ottoman Empire. Their primary culture must be Altaic or Iranian. They'd have to not be a vassal, and control Jaipur, Panipat, Delhi, Lucknow, and Agra, and have cores there. Leader needs a military score of 6, and country must be at peace.
If one is a nomad, the conditions are slightly different. They'd still have to not be Persia or the Turks, the primary culture still must be Altaic or Iranian. But they need only control the provinces mentioned above, don't need a core. Nomads can also form Mughalistan by vassalizing Khandesh, Delhi, and Sindh (all other conditions apply, but doesn't require you control any particular provinces if you've vassalized all three).
So, off my head, I think the easiest and most obvious choice is the Timurids (that's how it happened historically as well), though any horde with an Altaic primary culture can do it (even Golden Horde). Non-horde candidates would be Baluchistan and Durrani (I think they have an Iranian culture)... I can't think of who else.
Best you load a 1399 (or anywhere) start, load up a local nation (Delhi, Timurids) and see who has the correct primary culture.