Heat 3 tbsp of the olive oil in a 26 cm / 10-inch nonstick skillet with a lid over medium heat. Add the potatoes in a single layer and season with a pinch of salt.
Cook for 10 to 12 minutes, stirring every 2 to 3 minutes, until the potatoes are golden at the edges and tender when pierced with a fork.
Push the potatoes to one side of the pan. Add the remaining 1 tbsp oil and the onion, and cook for 2 to 3 minutes until soft. Add the garlic and cook for 30 seconds until fragrant.
Mix the onion and garlic into the potatoes. Add the diced tomatoes and a light pinch of salt and pepper. Cook for 3 minutes, until the tomatoes soften into a light sauce.
Scatter the halloumi cubes over the top and cook for 2 minutes, just until the edges soften.
Use a spoon to make 4 small gaps in the mixture. Crack one egg into each gap.
Cover the skillet, lower the heat, and cook for 4 to 5 minutes, until the egg whites are set and the yolks are still soft. Cook 1 to 2 minutes longer if you prefer firmer yolks.
Remove the pan from the heat. Scatter the mint and chili flakes over the top, add a squeeze of lemon, and serve straight from the skillet with warm bread.