If you are the one who gets to pick the topic for your Exploratory essays, then choose something that you already know well. This is the easiest and the biggest shortcut around. You already have the material in your head, ready to put it down on paper. Plus you will already have a few good ideas about where to search for more information. The things you know may be a little boring. You may know a few of Shakespeare's works or the story about manufacture of the "Titanic", but you consider them boring. In most circumstances, people know these sorts of things because they studied them at school. If they hadn't studied this information at school, they would have never researched them. In that case, if you are the one who is able to pick the Exploratory essay topic of your choice, then pick something that you enjoy. Choose something what you want to learn, or what already interests you. Use the Exploratory essay as a way of learning something that you want to know about.
It means that the best topics for exploratory essays are the ones that people often argue about. You can write about issues that aren’t agreed on yet, if you have enough information to do research on them. Here are some strong topics that can serve as examples:
How To Find Interesting Topics For Your Exploratory Essay