1. ''My supervisor considers his least favorite duty dealing with customers.''
Is ''dealing with customers'' ... an adjectival phrase?
*****
NOT A TEACHER *****
I have been waiting 24 hours for someone to answer the OP's question, for I, too, want to know the answer.
I have been checking my books and googling like mad. I have found some information that I think answers that question, but I do not have the confidence to give a "Yes" or "No" to that question.
"He considers his favorite
duty talking to famous people."
1. I believe that "everyone" parses a gerund phrase as a noun phrase.
2. One source gives this sentence: "Do you consider
memorization of vocabulary learning?"
a. The source says that the gerund functions as an NP [noun phrase].
3. In my research, I was reminded that the objective complement often implies a
copular relationship.
a. That is to say, the sentence actually means "He considers his favorite duty
to be talking with famous people."
i. And further refined: "His favorite duty
is talking with famous people."
(a) Most books would, I believe, label "talking with famous people" as a so-called
predicate nominative in 3ai.
The source for 2a is Ms. Nancy Sullivan in her 2014 book
Essential Grammar (thanks to Google).