Preheat oven to 400 °F.
Slice a thin piece off of the tops of potatoes lengthwise you want to slice off less than ¼ of the potato. Scoop out the potato flesh from both cuts of the potato into a mixing bowl and transfer the potato boats to a baking sheet. With a fork or potato masher, smash up the potato in a bowl until somewhat smooth.
Place a medium-size skillet over medium high heat with 2 turns of the pan of EVOO, about 2 tablespoons. Add the onion, garlic, some salt and freshly ground black pepper. Cook, stirring every now and then, for 2-3 minutes, until the onions start to get tender.
Add the reserved potato flesh and paprika to the skillet, stir to combine and cook, stirring every now and then for 2-3 minutes, until nice and golden brown. Add the hot sauce, corned beef and half-and-half or heavy cream. Heat mixture through and re-season with salt and freshly ground black pepper.
Pile the potato-corned beef mixture back into the reserved potato boats. Bake in the oven until the tops are lightly browned, about 5 minutes.
While the potatoes are browning up in the oven, cook up 4 eggs however you like them. Remove the potatoes from the oven and top each with an egg before serving.