Preheat the oven to 200C/400F/Gas 6.
For the stuffed pepper, place the black pudding slices into the pepper half. Place onto a non-stick baking sheet and bake in the oven for 10-15 minutes, or until the pepper is soft.
For the fried eggs, heat the oil in a frying pan over a medium-high heat and crack in the eggs. Season with salt and freshly ground black pepper and fry until the whites are set but the yolks are still runny.
To serve, place the stuffed pepper onto a plate and top with the fried eggs.