What topic do you pick?
Someone on my Facebook feed posed this question and I thought it was interesting.
How to bullshit your way through a 45 minute presentation with no preparation.
Homebrewing. I’ve been brewing since Carter legalized it, and have given many presentations fairly off-the-cuff. Heck, I’ve even done TV shows where the only prep was making sure all the equipment and supplies were on hand.
I could also probably give a 56 minute presentation of the court cases dealing with Freedom of Religion in this country, since that is the unit I am currently teaching to my seniors. 
History of the flag of Canada. I’ve done it in the past with prep time, but could easily do it impromptu.
[synthetic] Chemical-free lawn care.
French and Indian War; either
a) Soldiers life
b) George Washington from the viewpoint of the French
c) Money (its really about language and phrases that are still with us today)
d) Frances Slocum (OK - more Rev but still a good lesson)
These are four of the 8-10 “school programs” (usually given outside of schools if I’m being honest about it) that I have in my brain ready to perform at a moments notice.
Pick a current event that you’ve particularly been interested in, but is not too controversial.
Two-color knitting.
In school, my teacher assigned us an oral book report. Of course I blew it off until the day of.
I bullshitted my way through my presentation about WWII war planes. Completely making shit up. And I got an A+ for my troubles! 
As I’ve taught the same or similar courses for many years, I could do a pritty good job at many of those presentations with no notes.
This is my frickin’ life as a high school history/civics teacher in a chaotic school environment where I might be dropped into a strange classroom at a moment’s notice. Is it cheating to choose a topic where I recently prepared a 45-minute lesson? If not, and if I’m going for things where the topic is reasonably entertaining and I had plenty of extra stuff to fill time (most people tend to rush when doing a presentation without much preparation), I’d go with one of these:
- the origins and evolution of Chicano lowrider culture
- Enlightenment views of humanity’s “state of nature” and how they relate to different political systems (Hobbes versus Locke versus Rousseau)
- gerrymandering
- analyzing a few poems by Siegfried Sassoon and Wilfred Owen
- “Afro-Mexicans” — that is, Mexicans with significant African slave ancestry (at least a third this presentation would involve talking about colonial Mexico’s super-granulated racial hierarchies and how they persist today).
If I couldn’t cover a topic I’d done in class (more in the spirit of the OP), I guess the area where I feel like a layman expert would be democratic electoral/voting systems.
EDIT: OldGuy’s comment makes me think that teachers and the like don’t find this question very challenging.
“How to Find Porn On-line”, followed by 44 1/2 minutes of Q & A, and quite possibly uncomfortable silence.
We don’t. 
Weight training.
You know, I often have to extemporize in my classes. If I have a role model as a teacher, it’s James “Connections” Burke. The way my mind works, I can start talking about the main topic of my class… then come upon an interesting sidebar and start talking about that… and then be reminded of a funny related anecdote… where was I? Okay, back to the main topic, until I hit another sidebar, or get a question that reminds me of another topic…
For that reason, I tell all my classes on Day One, “The best stuff we talk about here will NOT be on the test.”
So, I not only CAN talk for 45 minutes abut things I haven’t studied or prepared for, I DO it often.
I could also pretty easily do 45 minutes on a topic in scope of one of the classes I teach (computer forensics or information security management). I’m teaching forensics this semester. I just regaled my students with a thrilling trip through the NTFS file system last night. I could repeat that off the cuff today if I had to 
Or I could pontificate on how to respond to computer security incidents for 45 minutes pretty easily.
Twenty years ago, I could probably do a decent 45 minutes on selected William Faulkner’s novels. I doubt I could do that today.
Funny. There was a (very bright) stoner kid in my debate class in high school. The best speech he ever gave was his “how to” speech on “how to BS a speech”.
(Incidentally, he’s now a “Friend” on Facebook, and remains very entertaining).
As for me…
If under pressure, I could ramble on about any number of topics (and easily get to 45minutes if “bullshitting” was permitted):
- The impact of Babe Ruth on baseball.
- The real estate closing process in Florida.
- The reasons for the Civil War.
- The criminal justice process in Colorado.
- The best QBs in NFL history.
- Nutrition and workout regimens for gaining muscle and losing fat.
- U.S. politics in the 21st century.
- Reasons for the rise of Trump.
- Estate planning considerations.
- What I would do if I won Powerball
The U.S. space shuttle program (for a non-engineer, non-space-geek audience).
(Sorry, Stranger: “STS” )
Horses or libraries.
I do 15 min a week on various distillery topics. I can do an hour easy by combining those topics. A couple of recent ones I’ve done:
How different fermentation bases affect the flavor and texture of the final spirit.
Still design
Process Heating and Cooling
Barrel maturation
Dust hazards and control
Distillery fire protection
After that I can talk about my opinion on lots of things at great length.