Report can be used transitively (report an issue) or intransitively (report to a superior).
Here it is used transitively and takes a the verb have (which then goes in the gerund having).
Have can be used by itself as an auxiliary or a transitive. Here it's used as an auxiliary, and auxiliary have takes a verb in the past participle. In the example, the next verb is have but it is in the present participle having instead of the past participle had. Even then, auxiliary had forming the perfect can't take another perfect-forming auxiliary have (but it can take the possessive have or obligation-indicating have to, for instance)
The only time I can fathom "having had [past part.] would be if I oddly moved a direct object from in between the string of verbs: "I have had made for me three dolls" —> "Having had made for me three dolls, I ...". But even then, it sounds quite old timey and still doesn't allow the second have to be in the present participle.