Carrot top  
Carrot muffins.  
Muffins  
Derpy.  
there.

@LasPegasusAce  
I wish I could upvote comments.

Rainbow Dash told Derpy that carrots are good for the eyes. They’ve been dating ever since!

@DanielTepesKraus  
Dammit I fell asleep. I should really get an All-Night Mask for stuff like this.

I, Vree, self appointed meme investigator on all things pony, can verify that @elosande’s piece that upanon posted (>>6785 (merged)) was indeed what started it back on /co/ (before the Great Diaspora to the rest of the internet, which you will be able to read in my upcoming book).
 
elosande comic -> fridge meme -> unrelated Derpy & Carrot BFF comics
 
This also explains for example why Raindrops (Derpy’s partner in the Feeling Pinkie Keen scene) was ingored; that scene did not exist back then yet.

@Anonycat  
actualy it seems to vary between author. one version has Derpy take carrot in after she gets a bad cold from working in the rain.

You can find the comic Anonycat is talking about here: >>6785 (merged). It’s also where Derpy’s fridge-emptying obsession came from.

@Anonycat  
Ah, right. Well BP, there you go.

@Jadefire  
They weren’t roomies, Derpy had crashed through Carrot’s ceiling and busted one of her wings, (she had to deliver a parcel and had the accident while she was checking a map) so Carrot Top convinced her to stay and heal while she delivered the parcel all by herself.
 
As everything during the earlier days of the fandom, this was enough to create it’s own fancanon and began expanding from there.

@HamburgerTime  
Of course, I’m more of a FRIENDshipper.

I like it.

:)

Basically, the fans saw Dinky Doo and decided shee should be Ditzy/Derpy’s daughter. Carrot Top was seen hanging around Dinky (and later Derpy) and we all thought “Wow cool”.
 
The end.

link to the carrot top vector?

And what a story it is! It’s a tragic tale of romance, passion and of murder most foul! Grab a seat, young foals, this is going to be good. Are you sitting comfortably? Good. Once upon a time, in the beautiful city of Canterlot, lived two happily married ponies named Dalton Hooves and Diana Hooves who had just had a baby. A beautiful baby filly with adorably crossed golden eyes, whom they named Derpy. As the years went on…
 

There was a comic that starred Derpy and Carrot Top as roommates, where the punchline was Derpy stating she emptied Carrot’s fridge.
 
As for why the comic decided they were roommates, I have no idea.

their housemates.  
as for how it started, it varies depeding on the wrigheter.

I think it started with that “I emptied your fridge” meme and escalated from there.

In my universe, it never did.

Well, first the Earth cooled…

Early on, same way that LyraBon started.