Probably not much. I think poetry from the Islamic world is fairly accessible, especially if you count the whole of the Quran. But Persian is fairly specific, and rather antiquated to boot.
So, I came across a small collection by Scholastic (circa 1975) at the local Goodwill. The book was a translation of poems of an 11th-century philosopher and scholar, and since it was cheap and uncommon-seeming I bought it. I was pleased, and suprised. Let me share a bit with you.
The Rubaiyat of Omar Khayyam:
Myself when young did eagerly frequent
Doctor and saint, and heard great argument
About it and about: but evermore
Came out by the same door where in I went.
The worldly hope men set their hearts upon
Turns ashes -- or it prospers; and anon,
Like snow upon the desert's dusty face,
Lighting a little hour or two--is gone.
Alike for those who for to-day prepare,
And those that after some to-morrow stare,
A Muezzin from the tower of darkness cries,
"Fools! your reward is neither here nor there."
Why, all the saints and sages who discuss'd
Of the two worlds so wisely -- they are thrust
Like foolish prophets forth; their words to scorn
Are scatter'd, and their mouths are stopt with dust.