Seeing an opportunity to bring the concept to New Zealand, he and wife Nadine went there to attend a frozen yoghurt "university" run by manufacturing giant YoCream, to learn the inner workings of "fro-yo".
Starting a business in New Zealand was essential for the 58-year-old Markgraaff to emigrate from his native South Africa.
"To be able to get a man of my vintage into this place I had to submit a business plan which, among other things, wanted us to employ a couple of Kiwis and establish a business that was not stealing jobs away from real Kiwis," he says.
He left behind his concerns about a rising violent crime rate, but also a business background in construction, property development and real estate.
With 30 years' experience in the real estate industry, Nadine says when she arrived in New Zealand she couldn't bear the thought of re-sitting all the necessary exams and going back to selling property.
Now the couple, alongside daughters Natalie van Niekerk, Chantal Janssen and Janssen's husband, Franswa, run a business that employs nearly 80, mainly young, New Zealanders.
The demographic of KiwiYo's customers, in line with international trends, is also younger, with the appeal of creating your own unique frozen yoghurt dessert drawing in the 12 to mid-20s set.
Whereas a traditional icecream stop may be an impulse purchase, KiwiYo is more of a destination for its customers.
"Our operation is actually a form of entertainment," says Markgraaff. "Kids can actually sit down on a Saturday afternoon and say, 'What should we do?'. They can say: 'let's go ice skate, let's go play tenpin bowling or why don't we go and have a KiwiYo?'."
Nadine says the KiwiYo stores provide a fun, safe and clean environment for an outing without being old fashioned.
Added to that are in-store cameras that allow customers to photograph and post their confections on social media, creating word of mouth buzz that has more than 20,000 "likes" on the company's Facebook pages and thousands of internet images.
The popularity of the stores has resulted in All Blacks tweeting about their visits, competitors covertly photographing and copying the operation and more than 600 people expressing interest in becoming franchisees.
Franchising the concept is the cornerstone to growing the store count to 26 by the end of next year.
Eight of those will be corporate stores - currently there is a KiwiYo in Botany Town Centre and another, in Takapuna, is set to open next month, as well as the original Mission Bay store - with the balance owned by franchisees. They are negotiating franchises for Tauranga and The Base shopping centre in Hamilton and nailing down a property deal for a site in Queenstown.
A cut-down version of the store, KiwiYo Express, which comes without the "paraphernalia" such as Facebook photo uploads, could be an option for smaller towns or beach locations, says Markgraaff.
"The reason that we're going the franchise route is that we can expand rapidly without having tonnes and tonnes of financial backing ourselves," he says.
"The difference between us and our opposition, from my perspective, [is] we want to sell a guy a franchise that he's going to make a good living out of.
"Our opposition wants to sell a franchise to make money out of the sale of the franchise."
He says franchising is about growing the business and not how they will grow revenue.
Expansion plans aren't limited to New Zealand. Markgraaff is in talks with Chinese, Indian and Australian operators interested in buying a master franchise for KiwiYo.
He says the Asian market has been "wild" about the concept and is "ecstatic" when they hear the yoghurt base will be manufactured in New Zealand.
Markgraaff originally floated the idea of offering Australian-made yoghurt in the Asian markets, but the response was an adamant "no-no".
In the longer term, Markgraaff could be back doing business in the country of his birth, albeit through a master franchise.
"So, when I burn my Springbok jersey I won't burn all the rest of the contacts."
Nadine says his Springbok jersey, a cheap knock-off bought in China, has a spelling mistake anyway.
