The present tense/active form of monologued. The act of delivering an involved stream-of-consciousness exposition or explanation, usually in an overly dramatic fashion, that completely halts the conversation. Like in a book or movie where the action screeches to a halt so the character can stand and deliver a huge load of backstory or explanation. Not always TMI or a rant, although those can be forms of monologuing.
Man, she just started monologuing and it was all over.