"What led to you doing this thing" grammar?

What you effectively have is a clause that fills the slot in a sentence ordinarily filled by a noun phrase.

Languages have various mechanisms for this. As in this example, a common structure in English is to have a clause with what is sometimes termed a gerundive form (effectively, an -ing form used in a syntactic structure that fills a 'noun phrase' slot but that internally is still ostensibly verbal-- e.g. can still have a subject and object, be passivised etc just like a normal verb). As you can see, a special feature of a gerundive clause in English is that the subject usually occurs in the oblique form, so e.g. "him" rather than "he" in the example below:

[Him doing this] is important.

[??*He doing this] is important.

(You can also get "his", although that's arguably just a prescriptive hypercorrection.)

Both English and other languages have other structures to cover this function. Romance languages, for example, have subjunctive forms that function in a very similar way. English can also employ a clause with an (explicit or implied) modal verb, or an infinitival clause usually introduced by "for":

What we need is [ for him to help us ].

[ That he should choose to help us ] was a surprise.

We requested [ that he (M) help us ].

where in one possible analysis, (M) stands for a 'null' modal verb.

In ‘you doing this thing’, ‘doing’ is a non-finite verb. Another way to express it is with ‘your doing this thing’, where ‘doing’ is a noun. The first emphasises the act of doing, while the second, which sounds rather more formal, emphasises that it was ‘you’ doing it.