There are a couple of aspects of Kingdom of Sheba that intrigue me before I even try its food. As I approach the restaurant in Bute Street in Butetown, Cardiff, I'm greeted by a small, squat, and dark grey building, with a flat roof, boxy shape, and hefty metal gate reinforcing its front entrance.

It reminds me strongly of the architecture of buildings in the Middle East and I can't help but think it's fitting setting for a Yemeni eatery. However it turns out this is purely coincidental: the building's former iterations include a Somali café called Taste and, at some point before that, an internet café.

Another interesting feature is its location. It's a short walk away from the main strip of businesses in Loudoun Square – among them a Somali diner called Togayo that is much-loved by locals. It admittedly feels rather disconnected from the main trading hub – instead plonked, like an incorrect jigsaw piece, on the edge of the Hodges Row cul-de-sac right in the middle of residential properties.

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Kingdom of Sheba's curious appearance is no doubt enough to snag the gaze of a passer-by but its main draw is its offering of authentic Yemeni food. For a tiny place that most in Cardiff have probably never heard of – and that has to compete with the restaurants in the Bay and city centre – it has built up a very impressive reputation. It's rated 4.8 out of five stars on Google, with glowing reviews commending its good portions, reasonable prices, and, most of all, its "fantastic and lovely" dishes.

I pay a visit on a Tuesday morning to try some breakfast. The interior is simple and mostly white, save for a mural depicting an ancient Arabian scene with the biblical Queen of Sheba herself (Sheba, her home, being a kingdom in southern Arabia, which was a region of modern-day Yemen). There are a few other customers but that's to be expected – the busiest day is Friday after everyone returns from the Jummah prayer in the mosque.

A smiley and chatty waiter, Mohammed Ali, takes my order and tells me the owner, Ammar Alshameri, is out buying fresh fish for the restaurant. He takes me through what dishes are on offer, apologetically informing me a written menu is still in the works, but enthusiastically promising me he can make me "anything you like".

I choose small pieces of lamb with flatbread along with some Yemeni tea. Other breakfast dishes on offer include beans, eggs, cheese, liver, and a Yemeni version of a fava bean stew called ful. As I wait for my food, which is being made by another employee in the back, Mohammed tells me it's his second day on the job. The 34-year-old, who is Yemeni himself, has lived in Butetown since moving from his homeland in 2009.

He used to work at a takeaway kebab shop in Barry but was a regular customer at both Taste and Kingdom of Sheba – "My breakfast is from here, my dinner is from here," he laughs – before he took up work here. His passion for the food shows throughout our conversation. “The food is hot and fresh. We cook it fresh and give it to the customer. Nothing is frozen," he says.

I also chat to another customer, Fuad Zaid, a 40-year-old support worker who has lived in Butetown his whole life. He is also Yemeni and visits Kingdom of Sheba around twice a week. When I ask him about the restaurant's standing in Butetown – which is one of Cardiff's most socio-economically disadvantaged areas and has a large ethnic minority community – he says: "It’s good because it actually has brought a lot of the Yemeni community out of their houses... It’s good to have these food places in our community... It’s culture, tradition and it brings the people together. People you haven’t seen for ages, you come in the morning and see them having breakfast."

There certainly is a strong sense of community in the restaurant. Mohammed exchanges greetings and conversations with diners and, later on, a customer chats at length with Ammar at the counter over a cup of tea. Outside there are some lone chairs and one elderly man takes a seat watching the traffic go by as he finishes off his drink.

Through an open doorway leading to the kitchen I see a flash of fire in a pan and shortly thereafter Mohammed brings out my meal. The lamb, cooked with onions and peppers, is accompanied by a simple lettuce, onion, and cucumber salad, a homemade chilli sauce, and a flatbread. It costs £6 and my steaming hot cup of Yemeni tea just £1.

I don't think I've ever had lamb for breakfast or brunch but after this I'll certainly be trying it again. The meat is juicy, not too oily, well seasoned with salt and cumin, and brightened up by coriander. It has a little bit of a kick to it though it is not overpowering. The chilli sauce – which appears to be chilli peppers whizzed with tomato and herbs – adds even more spiciness and is refreshing and zingy. My one gripe is the flatbread doesn't appear to be freshly made in the restaurant – and would no doubt be better if it was – but overall it's a tasty and great value for money meal that I would buy again.

The Yemeni tea is also delicious, fragrant with cinnamon, cloves, and other spices. Mine has been sweetened with one sugar, and, after I wait for it to cool, it's not too milky but rather light and refreshing.

Just as I'm finishing my breakfast Ammar, 44, returns, armed with shopping bags. I manage to chat to him for a few minutes in his busy day about the story behind the restaurant. He's been running it for nearly three years, ever since he left his old job at Tremorfa Takeaway and took over the lease from the owner of Taste. Like Mohammed he came to Cardiff in 2009 having moved from Yemen and hasn't been back home for 15 years.