Preheat your oven and thoroughly wash the potatoes to remove dirt. Pierce each potato with a fork several times so steam escapes during baking. Rub oil, salt, and pepper all over the skins to season and help them crisp.
Place potatoes on a baking tray and bake until tender and easily pierced with a fork. The skins should look slightly crisp and the inside fully cooked. This step builds the base texture for the dish.
Allow potatoes to cool slightly so they’re safe to handle. Slice them in half lengthwise and scoop out the soft flesh into a bowl. Leave a thin layer inside so the shells stay sturdy.
Mash the potato flesh with shredded cheese and seasoning until creamy and smooth. Taste and adjust salt or pepper if needed. The warmth of the potatoes helps melt the cheese into the mixture.
Spoon the cheesy mixture back into the potato shells. Create a small well in the center of each portion so the egg can sit neatly without spilling.
Crack one egg into each filled potato and return them to the oven. Bake until egg whites are set and yolks reach your desired doneness while the cheese turns bubbly and golden.