Is there any technical term for a type of reading that focuses on minor characters in a literary work? For example, a type of reading that focuses on the character of Polonius in William Shakespeare's Hamlet or on the character of Jordan Baker from The Great Gatsby.
This would probably be what is called a parallel novel. Common examples include Wide Sargasso Sea, Rosencrantz and Guildenstern Are Dead, and Grendel. To quote wikipedia:
These stories further the works of already well-known novels by focusing on a minor character and making them the major character
so it seems to be exactly what you're looking for.