"hablar" following "escuchar"

[Nfqufktc]

Here is an example (ex. 13.2, sentence 15) from the Complete Spanish Step-By-Step by Barbara Bregstein:

Nosotros nos callamos para escuchar hablar al experto que habla en voz baja.
We become silent in order to listen (pay attention) to the expert who speaks quietly.

I wonder if someone could point out the grammar rule that substantiates stringing one infinitive ("hablar") after the other ("escuchar"). To me "hablar" seems superfluous in this context.

Your help is appreciated.

[aleCcowaN]

Maybe I'm wrong, but I understand each verb in infinitive to be the direct object of the previous one

callamos ... escuchar
escuchar ... hablar

There are even longer chains

La codicia lo llevó a intentar hacer circular dinero falso.

Notice the subject doesn't change (the people who stop talking; the greedy guy) , thus enabling this kind of construction.

Regarding the apparent superfluousness, it is solved when we consider the specific meaning of hablar, here intended as to discuss or to address an audience, unlike the "que habla" part where it just means to speak.

Nos callamos para escuchar al experto may imply the expert may have been already talking, or we simply wanted to eavesdrop.

[Nfqufktc]

Thank you for your reply, aleCcowaN.

Would you confirm if my understanding is correct?
This part may be parsed as follows:

It looks a bit like the matryoshka nest-doll structure to me

[aleCcowaN]

I'm going to defer to our skillful moderators, Rusty and Angélica, who are more proficient than me in this subject and certainly will add their comments.

What the matryoshka-nest-doll structure made me think is the concept of inheritance in an object-oriented programming language, which Spanish isn't. In your analysis there is an experto que habla en voz baja as if opposed to a competing experto que grita como loco. I don't think that's the intention here and the whole subordinated clause is offered just to provide a cause to the whole action and breaks the chain, turning the inner portion of the nest-doll in a sort of jack-in-the-box.

But I better stop making this silly comparissons before a red balloon shows in the horizon.

[poli]

I think in this case that hablar works as a noun. Escuchar serves as a more traditional infinitive. (everyone quieted down to listen to the speech of...)