A midrash is a rabbinical interpretation of Scripture. This term is sometimes used interchangeably with aggadah. However, aggadah suggests more strongly a story. So when I am using it, I am referring to an interpretation of Scripture that is done in the form of a narrative reworking of a passage. As such, there is filling in of gaps in the Biblical stories. Some would reject this idea, suggesting that doing so is “adding to Scripture.” The fact is that any interpretation is in some ways an adding to Scripture. The key to a good midrash is that it is done with humility and make it clear that the story is tentative. Frankly, all theology is supposed to be humble and tentative.
Here are a few articles I have done before that could be thought of as speculative interpretations of a Scripture passage. One of them, “Reflections on the Waters of Bethesda” is the one that most closely aligns with this. The others reflect theologically in different ways.