In a large non-stick frying pan over medium heat, cook the bacon and sausages until they are browned. Reserving the fat in the pan, transfer to a heat resistant dish. Keep warm in the oven.
Fry both sides of the potato and soda farls in the reserved fat for a few minutes, or until they are golden and crispy. Meanwhile, heat oil in smaller frying pan over medium heat and cook black pudding slices and tomato halves. Transfer everything to the dish in the oven to keep warm.
Crack eggs into the pan with any residual bacon grease, adding more oil to the pan if necessary. Fry until egg whites are set but yolks are still runny, or to your liking. Divide everything onto 2 separate plates and serve immediately.