Should professors with Chinese names be addressed with surname only or both names?

Being an Asian myself, I'd use 'Dear Prof. Zhang.'

In Chinese culture, it can be considered rude for a junior to address their senior by the full name, that's just the way we're brought up to address our seniors, well at least for me...

In the United States, at least, one would typically use the same structure of address as with any other name, e.g., "Prof. Zhang." To do otherwise marks the person as different in a way that may be inappropriate, particularly if (as with many Americans of Chinese heritage) they use a European name order. If the professor wishes to be addressed otherwise, it is up to them to make this clear. From my experiences with European colleagues, I would expect it is similar there as well. I cannot speak for proper courtesy in East Asia...

Rule #1, ask the professor if you are unsure. Ask him what name he prefers to be called. I am a Chinese and a native Chinese speaker. I myself always like Westerners to ask me this question before they call my name.

In the example you provided, both Zhang and Yi can be used as English translation of Chinese surnames. Zhang is a popular Chinese surname and Yi happens to be one of my relative's surname. As you can see in this example, it's easy to make a mistake when calling Chinese names. Not to mention that the Chinese name convention is Surname first and Forename last (or Last name first and First name last).

If you cannot ask him for whatever reason and you have strong reason to believe that his surname is Zhang, you should call him Dr. Zhang. This would be the most appropriate way.