Shaykh Ibn Uthaymin (may Allah have mercy on him) said that Eid sermon is only one, is there any scholar who preceeded him in saying this? May you please tell me which scholar said this mentioning the book that I can find this in, its chapter and page number? What is your opinion regarding this issue? May you please provide proof? خطبة العيد واحدة أم اثنتان؟

In the name of Allah, The Most Gracious, The Most Merciful.
The generality of scholars are of the opinion that Eid has 2 sermons. There are many scholars who said thagt there is consensus on tis issue, among them Ibn Hazm in his book al-Muhalla (3/293).
Despite engaging in an extensive research, I have not come across anyone who stated that there is only one khutbah for the Eid prayer. No one from the jurists of the mathabs and other scholars said that. However, this view can be inferred from the words of as-San'aani who mentioned in his explanation of the hadeeth of Abu Sa'id (may Allah be pleased with him) that he said, "The hadeeth contains the fact that the Prophet (peace be upon him) used to go to the place for performing the Eid al-Fitr and Eid al-Adha prayers. He would start by performing prayer. Then he would stand facing the people who will were seated in rows. Then he would exhort and command them" In Subul as-Salaam 2/140, he stated, "The hadeeth does not mention that the khutbah for the Eid prayer consists of two khutbahs like the Friday prayer, and that the Prophet (peace be upon him) sat down between the two khutbas. Maybe this was not established based on the actions of the Prophet (peace be upon him). Probably, people made two khutbahs on Eid based on comparison to the Friday prayer.
By looking at the sayings of Jurists and scholars it is clear that they compared it with Jumah and they mentioned proofs which support their view. They deduced from a hadith narrated by Ibn Majah on the authority of Ismail Ibn Muslim from Abu Zubair from Jabir who said:
“The Messenger of Allah (peace be on him) went out on the Day of Al-Fitr or Al-Adha, and delivered a sermon standing up. Then he sat down briefly, then stood up again.”
There is unanimity that Ismail Ibn Muslim is a weak narrator.
Another proof they used to deduce is a hadith narrated by al-Bazar in his Musnad on the authority of Sa’d Ibn Abi Waqas who said that:
“The Messenger of Allah (peace be on him) used to deliver two khutbahs standing, and he would separate them by sitting.”
Al-Haithami said in Mujma’ al-Zawaid (2/203): “There are people that I don’t know in itschain of narrators”
Al-Nawawi said in al-Khulaswah: there is nothing established repeating the sermon but what is considered is analogy between jumah and eid.
This is the best I have come across. Maybe our Shaykh Muhammad al-Uthaymin (may Allah have mercy on him) came across an explicit text than these which conform to the ahadith indicating that eid has one sermon, and he mentioned the difference of opinion regarding this issue many times and he said the preponderate view is that eid has one khutba.
And Allah knows best.

Your brother,
Dr. Khalid al-Muslih