Prepare the black pudding: Remove the casing from the black pudding if it has one. This is usually quite easy to peel off. Once the casing is removed, slice the black pudding into rounds about 1cm (just under 1/2 inch) thick. Aim for even slices so they cook uniformly.
Heat the pan: Place a non-stick frying pan over medium heat. Add the butter or cooking oil to the pan and allow it to melt and heat up until it shimmers slightly. Don't let it smoke.
Cook the black pudding: Carefully place the black pudding slices into the hot pan, ensuring not to overcrowd it. You may need to cook in batches depending on the size of your pan. Let the slices cook undisturbed for about 3-4 minutes on the first side, until a beautiful golden-brown crust forms.
Flip and crisp the other side: Using a spatula, carefully flip each slice of black pudding. Cook for another 3-4 minutes on the second side until it's equally crispy and golden brown. You can gently press down on the slices with your spatula to encourage even crisping.
Season and serve: Once both sides are perfectly crispy, remove the black pudding from the pan. If desired, sprinkle with a little freshly ground black pepper. Serve immediately while hot and crispy.