Though in this case, I don't there's any champion who runs this build or anything close to it? AD champions might use 1-2 items from it but go into AD items; tank champions might use 1-2 items from it but go into tank items; AP champions might use 1-2 items from it but go into AP items; etc.
So, maybe it is still a bit trollish, but the build has some merit to it.
Basically, you run Manaflow Band with Presence of Mind (can run biscuits, but biscuits give less total mana). The core of core items is the manamune.
And from there, you build as many as you fancy, of, {Essence Reaver to replenish spent mana, Iceborn Gauntlet, Frozen Heart, Abyssal Mask, Righteous Glory}. You can theoretically build all five but that'd leave you without boots.
The idea of it is obvious enough. Get the highest possible amount of mana--and due to the way muramana works, mana = damage. The more mana you have, the more damage you deal. Basically--every time you autoattack or use any of Ashe's abilities (I think it is legit any of them!), you deal 6% of your current mana as physical damage.
824 base mana.
+1000 mana from Manamune itself.
+300 from Abyssal Mask.
+500 mana from Iceborn Gauntlet.
+300 mana from Righteous Glory.
+400 mana from Frozen Heart.
3324 maximum possible mana--6% of that as bonus damage is 199.44 bonus damage, on every attack, with essence reaver keeping you topped off.
Add in 250 mana from manaflow band.
And 500 mana from presence of mind.
That's 4074 maximum mana, 6% is 244.44 bonus damage, on every attack.
2400 from manamune + 2700 from frozen heart + 3000 from abyssal mask + 2700 from iceborn gauntlet + 2650 from righteous glory = 13450 for five items. A little bit expensive.
And I imagine that this build doesn't give the maximum amount of damage.
It's called a troll build for a reason.
But I think that you can see where the theory of the idea is.
Manamune gives the damage.
This build has built-in absurd levels of tankiness. Abyssal Mask gives MR and health; all the other items give armor. Frozen heart slows enemies' attacks and gives you cdr; iceborn gauntlet caps your cdr at 40% while also slowing their movespeed; righteous glory also gives (wasted) cdr but gives health and health regen; between all of these Ashe would be ridiculously hard to kill while dealing absurd damage.
Essence Reaver on top of that would give a further 20 (wasted) cdr, but the passive would mean that half of the mana spent on manamune would be refunded. (Manamune drains 3% per attack, essence reaver refunds 1.5% per attack.) Muramana gives 15% of spent mana back anyway, which means you get over half of your spent mana back.
Also, speaking of that--the 244 bonus damage is from the second passive. On top of that is 2% of 4074--81.48 extra + 244.44 as the maximum amount an attack can give = 325.92 the most you could deal in bonus damage.
Muramana and Essence Reaver between them give a bonus 105 attack damage. So Ashe would have 111.32 attack damage + 105. With a 25% crit chance for her slow, which would be a 30/60% slow applying her bonus damage which I'm too lazy to calculate. 325.92 + 111.32 + 105 = 542.24 attack damage per hit, plus the slow damage, plus crit slow damage.
Not to mention if you take transcendence then because you've got 30% cdr above the max...that's 30 * 1.2 = 36 extra damage on top of that.
Would I ever be able to run this build to completion?
Oh hell no.
Would it be fun to try? Hell yes it would!
I know.
Not optimal build. Especially not on Ashe.
But it has merit to it.
Deals decent, even if not maximum possible, damage.
Has cdr.
Has ridiculous armor and decent MR.
Has some health and health regen.
Slows enemies down a ton.
Allows you to stay in lane for almost forever.
Regardless of precision/sorcery first, you can presumably get some lifesteal from bloodline, allowing for replenishment of hp to some extent (a weakness).
Has flaws of no attack speed and limited movespeed.
Has the flaw of being hella expensive and time-consuming to execute.
Is a build geared towards the lategame and stalling it out to the maximum degree pretty much.
There's flaws to it, reasons why it wouldn't work.
But I think that if you could get it going, it'd be really fun.