MELBOURNE, Australia — Brunswick Street in Fitzroy is known as Melbourne’s epicenter of hipsterdom, a stretch of boutiques and bars and cafes catering to the young and fashionable. In many ways, Saba’s, a restaurant that sits smack in the middle of it all, adheres to the neighborhood’s trendy reputation. The design is sleek and simple, with bright pops of color on the wall in the form of vibrant woven plates. The customers are youthful, as expected, but the crowd is far more diverse than it is elsewhere in the area.

Saba’s, an Ethiopian restaurant, is run by Saba Alemayoh and her mother, Tekebash Gebre. Ms. Gebre grew up in Ethiopia, but spent 13 years in Sudan working as a maid and cook, before immigrating to Australia with her young daughter, Ms. Alemayoh, in 1999. Ms. Gebre’s home cooking became legendary among friends and family, and a restaurant was the next logical step.

Ms. Alemayoh recalls a childhood of trips to Ethiopia to visit family, returning to Australia with suitcases packed with spices and traditional Ethiopian teff flour, brought in part to cook for a sister who has celiac disease. (Teff flour is gluten free.) Saba’s opened in 2015, and Ms. Gebre remains the restaurant’s main cook, with two cousins helping out as needed.

The menu declares that the people in the kitchen cook from their own knowledge and have no written recipes. “Hope that they don’t get sick!” it jokes, which on first read seems like an alarmingly honest admission about the perils of food-borne illness. But it is meant to say that if Ms. Gebre and her family were unable to come to work, the restaurant would have no food. There is no recreating the recipes held only in their minds and hands.