Mata Parvati Making Ganesha | lord Ganesha birth story

According to the puranic myth, Airavata, the divine elephant of Lord Indra, was born on Earth due to a curse, and it was to give it salvation and restore it to its divine abode, that Lord Vishnu's Chakra (Sudarshana) touched the elephant. In fact, it was not slaughtered, instead the body of the elephant vanished keeping only the head, which was placed on Parvati Nandan's headless body and by the divine intervention of Lord Rudra (Shiva), our beloved Gajanana Sri Ganesh emerged. Also Airavata got moksha and returned back to Indraloka.
To answer, why Parvati Devi didn't create another Ganesha, there is a deeper meaning to it, a strong message given to the world by Parameswara and his divine consort. Parvati's creation was for benefit to the world, but in creating Parvati - Nandan (Please note the noun I am using for Ganesha before and after getting elephant face!) had two inherent flaws:
a) The boy was created without the knowledge of Lord Shiva, who is her husband. He is still Parvati Nandan alone.
b) Secondly, after birth, She failed to introduce him to his father. One might argue that Shiva is Omnipresent, so he would be aware, but this is a part of his leela (divine game), and he is "unaware" about his "new-born" son.
This may seem small thing, but it lead to a battle between the father and the son, and "untoward" incidents followed which is not in the scope of discussion now.
After Parvati-Nandan was beheaded, the Universal mother realized the flaw. To preach the world that "Every kid is a combination of both father and mother", Lord Shiva revived the boy with the "Pranava" - (Omkara) energy, thus making him Ganesh, Shiva-suta (Son of Shiva) and Parvati-Nandana.
Creating another Ganesha again singlehandedly by Parvati Devi, wouldn't have sent the right message. Instead of enlightenment , it would have introduced another flaw and not set the correct example.
In Tamil folklore, there is a saying, "It is the Mother who tells the kid who his father is, that's one of the reasons she precedes the father in the list of Obeisance in an individual's life. (Matah Pitah Guru Deivam) " This is an incident which highlights the aptness of that saying, and importance of both the parents in one's life.
On a lighter note, Ganesh ji was destined to get some many boons from all the gods, become agra pooja adhikari (Worshipped befote Trinity Gods of Hinduism), pratham pooja adhikari(Always first worshipped) and Ganadhyaksh (President of all the Shiva Ganas), so another Ganesha was not created :)
This incident made Ganesh ji, something not many people are aware of. Ganesh ji became Pranava Swaroopi, the one, who resembles the shape of "Om" - The Ultimate Pranava Mantra. Both Om and Lord Ganesha are same. This can be seen in references in Atharvasirisham, and compositions by Dikshitar, "Pranava swaroopa vakra tundam - Vaathapi Ganapathim ".