The quiz with a single essay question....what does it not have that you want?
The normal Moodle quiz can do that. And, if you really want to make sure no student jumps ahead, when setting up the quiz in the Grade section, set Attempts allowed to 1. Once everyone has completed the quiz and you have graded them, bump the Attempts allowed to 2. And so on...
When you go look at the quiz Results > Grades you will see all the attempts for each student.
Emma, I assumed that if they retook the quiz, then their previous attempt was deleted. I set this up last week for 48 students not quite thinking through what I wanted.
So, I'll try what Al says. Increase the attempts to 2.
Thank you.
-Derek