On Pitt Street in the CBD a blue button sits next to an unmarked silver door. When pushed, it grants entrance to an underground Nordic restaurant. In Caringbah an NY-style pizzeria has a strangely placed fridge door that leads to a sports bar and diner. On Enmore Road, a North Indian and Pakistani restaurant writes a secret menu every day on the back of a receipt docket – the only way to know what’s on it is to overhear someone asking for it.

For Penelope (Pepe) Marshall, co-owner of Superfood Sushi on King Street in Newtown, secret menus are a fun way to discover new foods. She’s just released her own off-menu special. “I’ve never done anything like this before,” she says. Pepe’s secret item is called the East Meets Mex, and you won’t find it instore or on any specials board. The only place you can get it is via Deliveroo.

“It’s a sushi burrito,” she says. It’s a huge hand-sized sushi roll. “We’re using rice with nori on the outside as the burrito wrap. Inside we’ve made a Tex-Mex mixture of black beans, chipotle and jackfruit.”

The rise of food-delivery services like Deliveroo has granted unprecedented access to a range of exotic menu items, which can all be enjoyed at home. Marshall believes exploring as-yet-undiscovered dishes is vital. “Sometimes I think it’s the only way to expand your horizons,” she says. “If I find a new food and don’t know what it is, I just give it a go. I’ve gained some real favourites over the years by trying something I didn’t know.”

Pepe recalls finding an Egyptian restaurant while travelling in Singapore, and discovering ful – a Middle Eastern breakfast dish of fava beans with cumin, parsley, garlic, lemon and chilli. “I had never tried it before in my life and I fell in love with it,” says Pepe. “I make it at home on a regular basis now. I’m an absolute convert.”

With the East Meets Mex, Marshall is excited to try out her first secret menu item. It sounds strange from the description, mostly because it features jackfruit, but Pepe says that’s intended to take on the traditional role of the meat. “It’s green jackfruit,” says Pepe. “We cook it with various herbs and spices and then it’s pulled. It has the texture and look of pulled pork but it’s all vegan.” It looks like a sushi roll, is wrapped like a burrito and tastes somewhere in between. Marshall has been eating it for breakfast and says those ordering it through Deliveroo should look for her other off-menu secret: a drink infused with aloe vera, mint and lime. “I love that sort of stuff,” says Pepe. “Only through word of mouth.”

The East Meets Mex sushi burrito is no longer available.

This article is presented in partnership with Deliveroo.