Should I use both surnames when addressing a Spanish professor as 'Dr' in an email?

Mexican here!!

We also have two surnames, and to be perfectly honest we do not mind if you use both or only one of our last names.

People call me Dr Palafox and my former advisor (Who is the head of the CS department) Dr Benitez. We are talking people from all the spectrum of workers, from administrative and cleaning staff to general directors. So is perfectly fine to use only one last name.

Actually is going to sound weird if you end up using both names, because we rarely do. Even the President is rarely called by his 2 last names, unless is a very specific situation.

You cannot do any harm if you are more polite when writing to someone with a significantly higher academic state than yours. So unless she's ever written you a mail signed less formally, stick to the formal way of writing.

It's actually quite unlikely that she gives any attention to it. When she replies, the way she signes at the end is how you should title her next time, with "Prof." added, which she'll very likely exclude.

Example:

You write: Dear Professor Doe-Toe, ... Sincerely, John Brown

She replies: Hello, ... Regards, J. Doe

Next time you write: Dear Prof. Doe, ... Best regards, J. Brown

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There are people who are really really informal. One professor at my university always uses just the first name at the end of e-mails. She really does not care, but politeness in my environment (Czech) says that you shouldn't reply so much impolitely.