Preheat the oven to 375°F (190°C).
In a large heavy bottomed skillet, add 2 tbsp (30 mL) of the olive oil; place the skillet over medium heat for a few minutes. Once the oil is hot, add the onions and peppers; cook for 5 to 6 minutes, stirring often, until softened.
Add the lamb to the skillet and break it up using a wooden spoon. Cook, stirring often, until the lamb is browned and the juices start to dry up, about 6 to 7 minutes. Add the garlic, cumin, paprika, chilli flakes, salt and pepper; stir to combine. Cook until the garlic is fragrant, about 2 minutes.
Add the tomato paste and crushed tomatoes and stir to combine. Cover with a lid and cook for 5 minutes.
In a separate small pan, heat the remaining 1 tbsp (15 mL) olive oil. Place the halloumi cubes in the pan and fry for 30 seconds on each side, until deeply golden. Remove and set aside.
Add half of the halloumi to the large skillet. Create 5 evenly spaced wells in the lamb and tomato sauce mixture. Crack the eggs one by one, placing an egg in each well. Carefully transfer the skillet to the oven and bake just until the whites are set and opaque but the yolks are still soft, about 6 to 8 minutes. Remove the skillet from the oven and allow it to cool for 5 minutes.
Garnish with the remaining fried halloumi cubes and parsley. Serve with pita bread.