What part of speech is The eating of generosity?

The term "The eating of generosity..." is a noun phrase, a group of Words based on a noun that functions as a noun in a sentence.

A noun functions as the subject of a sentence or a clause, and as the object of a verb or a preposition.

Examples:

The eating of generosity is the rule that she lives by. (subject of the sentence)

The message that the eating of generosityexpresses is self interest. (subject of the relative clause)

Overindulgence will put an end to the eating of generosity. (object of the preposition 'to')