We arrived, we ordered, the table filled with a brunchy gaggle of colourful dishes. And then I noticed something. Without even trying to, we'd kept meat to a minimum. More and more, Melbourne eateries are making it possible to be an accidental vegetarian, even if only for one meal. It's simply because the non-meat dishes are so good.

We were at Miss Kneady, a new all-day diner in a middling Templestowe shopping strip. But these weren't workaday breakfasts. There was a mushroom ragu over sweet, soft creamed corn, topped with a poached egg and toasted, herbed crumbs. The play of ooze and crunch was satisfying, the flavours and colours were comforting and cosy.

Poachies under hollandaise came with a choice of pancetta or smoked salmon but the veg elements dominated: the eggs jiggled over a sweet potato hash and the plate was brightened by green pea puree.

There was also a cauliflower frittata topped with braised eggplant and shaved fresh carrot strips, a riotously delicious and veg-heavy way to start the day.

It all starts to make sense when you know that Attil and Mark Filippelli are among the owners of Miss Kneady. These same brothers started game-changing vegan cafe Matcha Mylkbar (famous for vegan "eggs") and plant-based city patisserie Weirdoughs (famous for its no-lobster lobster roll).

They also own the Last Piece, the family-friendly Waverley Park restaurant that – over eight trust-building years – lured many locals away from boring big breakfasts to acai bowls and quinoa cakes.

That's not to say that the Filippellis are vegan evangelists; the Last Piece does porterhouse and pork ribs aplenty. It's just that they're canny trend-watchers and see the plentiful possibilities of plant foods. Templestowe is now in their sights.

The "kneady" has a couple of meanings. It's a reference to dietary needs, a challenge for every restaurateur, and one that Miss Kneady has addressed front on. As well as the vegan and vegetarian options, there are generous offerings for those going gluten-free.

That brings us to pizza dough, the kneading of which is also referenced in the restaurant's name. Many pizza joints buy in their gluten-free bases but not here. They're made in house by pizzaiolo Anthony Stagliano who ferments all his pizza bases over 72 hours, then cooks them in a fierce 45 seconds in a wood-fired oven that stands handsomely at the rear of the restaurant. Vegan soy-based cheese is available but Stagliano also makes mozzarella by hand.

Pasta, arancini and meatballs are crafted out back by nonna Rosa, who works alongside head chef Jamie Evans. His rich 36-hour beef shin ragu is tumbled with Rosa's rigatoni to create a rich, sustaining wintry pasta dish that's available lunch or dinner.

It's not easy to create a restaurant that feels good from 7am through to late. Miss Kneady does a decent job of it, accented in pink, with a central bar and flexible spaces for groups of all sizes and ages. Well-spaced tables seat 120, plus there's room for 50 more in the footpath gazebo.

It's bright, fresh and friendly, with a customer-focused approach that's likely to build the trust that leads to more adventurous diner choices. Basic breakfasts begone!

Rating: Three and a half stars (out of five)