Stepping in for Sensible Shoes, if that's the appropriate metaphor for the circumstances.
Sometimes you get to a point in the story where you just can't avoid an Infodump. The reader, and usually a character as well, needs to know some information and so you have another character tell them. And there's nothing wrong with that. But usually you don't want the exposition to become a monologue; an extended block-o-text that stops the action while everybody sits and listens.
Some writers can get away with it. No one ever complains about Father Mapple's sermon in Moby-Dick. (On the other hand, Father Mapple's sermon has the virtue of being lively, as opposed to some of the more technical passages elsewhere in the book). And Dr. Fell's Locked Room Lecture from the John Dickson Carr novel The Three Coffins is a legendary analysis of that genre, despite the fact that brings the narrative to a dead halt and adds little to the solution of the mystery. John Galt's speech in Atlas Shrugged is legendary too, but not in a good way.
But there are other ways to deal with the big block of exposition.
I recently wrote a play for a local church's Vacation Bible School program that involved various animals mentioned in the Gospels telling of how they encountered Jesus. By it's nature, the play had each animal telling an extended story, and were I writing it as plain prose, I could have easily gotten away with each story being a stand-alone unit by itself, like the stories which comprise The Canterbury Tales.
But doing it that way in a puppet play would be boring for the audience and tiring for the puppeteers. So, I broke up each story to let the other animals react to it, comment about it and ask questions.
This served several purposes. For one, it gave the other characters things to do while the one telling the story had the spotlight. It added variety to what would otherwise be an unrelieved monologue, helping to hold the audience's interest. It also gave voice to questions the audience might have and gave the speaking character the opportunity to amplify and expand on what he's saying.
But the reason I was most conscious of while I was writing the play, was that having the other characters comment on each story as it was being told, allowed me to reveal their personalities by how they reacted. The other characters were not just a passive audience, but engaged with the speaker and participated in the exposition.
So that's the theme of the exercise I've selected for tonight.
Your Protagonist encounters another character who tells him something. It could be information the Protagonist will need; it could be the character's life story; it could simply be an anecdote the character wishes to tell.
Have the Protagonist interact with this narrative. It could be by commenting on it; it could be be asking questions; it could be non-verbal reactions, or unspoken thoughts. If you still have your list of Things Your Character Wants from last week, you might see if some of those might affect how your Protagonist reacts to what he is being told.
Belinda was forced to miss the Ambassador's Ball, and so must hear about how her rival Adelaide appeared there with her beloved Lord Postlethwaite-Praxleigh (pronounced Puppy), from her loquacious neighbor Lady Natterby.
The Callow Youth and Stout Companion, still slogging through the inpenetrable swamps, encounter an Old Man in a Tree who knows something about The Jewel of Togwogmagog / Least Grebes / the Beldame of Onionset
Private investigator Celia Spunk's new client explains why he need protection from the Chainsmoke Killer.
International superspy James Buns is briefed on his latest assignment by his superior, Aunt Prudence.