Slice the Black Pudding into 1/2-inch (1–1.5 cm) rounds so each piece cooks evenly.
Heat a large nonstick or cast-iron skillet over medium-high heat and add a tablespoon of Vegetable Oil with a knob of Butter so the pudding browns without sticking.
When the fat is hot and shimmering, arrange the pudding slices in a single layer and fry undisturbed for 3–4 minutes until the edges are crisp and deep brown; flip and cook the other side for another 2–3 minutes.
Transfer the browned pudding to a plate and reduce the heat to medium-low; if the pan is dry, add a little more Butter or Vegetable Oil.
Crack the Eggs into the pan—cook sunny-side up for about 3–4 minutes until the whites are set but yolks remain runny, or cook to your preferred doneness (cover the pan for firmer whites).
Season the eggs and pudding with a pinch of Sea Salt and freshly ground Black Pepper to taste.
Serve the fried eggs on top of the warm black pudding and spoon any pan juices over the top. Enjoy immediately while the pudding is crisp and the yolks are luscious.
