So popular that "since the BuzzFeed article came out, we've had two hour queues at the weekend", owner Maria explains. "I actually emailed Mary's Milk Bar in Edinburgh to get their advice on how to cope".
Instagram has also helped spread the word.
"On Saturday we sold over 200 freakshakes", Maria explains. "We've been running out of ice-cream on several occasions. We're going to buy a bigger freezer".
When we visited Molly Bakes on a Thursday morning, there were six customers, all waiting to get a freakshake at 11am. That's dedication.
But Molly Bakes' success has been a long time coming.
"I started the company seven years ago, when I lost my job" Maria explains. "I had so much free time, so I just baked and baked. My auntie owns a bakery in Cyprus, but I never considered it as a career. After six months of making cakes for my friends, friends began to say you should sell those!
Maria took a stall at Brick Lane market, and soon moved to a commercial kitchen. Two books later, they opened a full-time premises in Dalston.
The freakshakes took a lot of experimentation to perfect.
"We ate quite a lot of milkshakes during the trial period", Maria explains.
"The milkshake base isn't enough to support the weight of the baked goods, so you have to add a dollop of ice cream at the top. And whipped cream helps everything balance."
And all the baked goods are made in-house.
Including the marshmallows. Which are then blow-torched to make them extra gooey. And yes, that's a homemade ice cream sandwich on top.
Crucially, the ice-cream base never changes.
"We use vanilla ice-cream for the base of each shake", Maria explains. They then add flavourings for each shake (fresh raspberries, peanut butter, or honeycomb) and milk. The only exception is the chocolate shake, which uses chocolate ice cream as its base. Each shake takes about five minutes to make.
Customers are loyal, naturally.
"We have customers who come in weekly", Maria explains. "We only have space to seat 20 people, but we're going to add benches outside for the summertime."
But nobody was expecting the shakes to take off in the way they did.
"We launched the freakshakes on Instagram at the end of January, with a day's notice. But somehow blogs got a hold of it, and we had a 200 person queue!"
As for plans for the future? They're not thinking that far ahead.
"I've never really had a business plan in my head", Maria says. "But maybe we might bring in some more flavours."