You have to know a thing or two about a thing or two to open a 170-seat cafe, get smilingly swarmed by a hungry public, and make the whole caboodle hum from day one. Levi achieves the improbable because it has experienced hands at the helm, a humble approach, and a hot chicken roll that's so good it's been popping into my mind any time (3am), any place (hairdresser), always inconveniently.

Co-owner Harry Butler is a carpenter who created his first cafe (Frank's in Cheltenham) because he couldn't afford a house. All that smashed avocado, you see, so he started selling avo instead. He's teamed up with cafe manager Kellie Buntz and coffee guy Lucas Sproson to turn a sewing factory into an amazing hangout for the people of Murrumbeena – it's raised the neighbourhood bar as high as the overbearing skyrail across the road.

The room is long, allowing for a courtyard at the front with retractable roof: grab a stool for smoothies or spritzes in the sunshine. Inside, there's a convivial mixture of tables for groups small and large, comfortable spots for solos, and a fab kids' lounge with beanbags, toys, even a little climbing wall – if the kids are metaphorically climbing the walls, send them in to do it literally.

It's hard to find good staff so it's something of a miracle that Levi has opened with a necessarily large team who all seem invested in the place. The message from management seems to be "say 'yes' if it's at all possible". That makes for a happy buzz (some may find it too loud at busy times).

Great food helps, too. Chef Emma Jeffrey has done it all: she played at the pointy end of fine dining with Gary Mehigan and Raymond Capaldi at Fenix, and was sous chef to a green George Calombaris at Reserve.

You know how cafe food got so great in Melbourne? Jeffrey was part of that, too, upping the ante at on-trend places such as Mammoth and Gilson. She's bringing all her smarts to Levi, working up a menu that's highly approachable but riddled with clever tricks.

The hot chicken roll is case in point. The trashy tradie trope is luxed up with beautiful roast chicken and herby stuffing, loaded into a fluffy potato bun with shoestring chips and chicken skin crumble.

A rich, chive-flecked jus is in a little pot on the side – made over three days, you couldn't find a cheffier gravy in Melbourne. Pour it over the roll or dip in: get messy, get glad.

There's another epic sandwich. The eggplant toastie is a succulent riot of curry flavours and lemon zing. It comes with a green chilli vinaigrette I'd be happy to bathe in.

Every cafe needs a sweet dish. Levi's is a brilliant breakfast pavlova. The meringue is perfect: crunchy outside, chewy within. It's filled with hot white chocolate mousse and topped with mandarin granita, freeze-dried mandarin and peach mousse. Honestly, you'd be happy with this in any great restaurant.

The chilli eggs are next level too. Jeffrey makes a base of peri-peri tomatoes, capsicum and pickled chillies: it's got loads of flavour. Herbed yoghurt, poached eggs, slow-roasted sesame seeds and clarified butter round out the picture. It's the very best of Turkish eggs married with the smartest of Melbourne spin.

Good food, good service, good place: it's a powerful trifecta. But what I love even more is that Levi feels just as chuffed to be in the neighbourhood as the locals are to welcome it. It's supporting Murrumbeena with cheery, fun times, one latte, one chicken roll, one warm "hello" at a time.

Rating: Four stars (out of five)