Put a medium nonstick skillet over medium heat and add 1 tablespoon of the butter and the oil. Peel and grate the potatoes on the large holes of a box grater or in a food processor. Sprinkle the potatoes well with salt and pepper and toss to coat. When the skillet is hot, add the potatoes, pressing them down and flattening them out to evenly cover the bottom of the skillet. Cook until the potatoes are well browned on the bottom, monitoring the heat as you go so they don't burn. Carefully flip over the pancake, keeping it in one piece, and brown it on the other side. Remove to a paper-towel-lined plate and keep warm.
While the potatoes are cooking, put a small skillet over medium heat and add 2 tablespoons of the butter. When the butter has melted, add the shallot and cook until it softens. Sprinkle over the flour and cook for a minute or 2. Pour in the cream and bring to a boil. Add the whiskey and bring to a boil. Reduce the heat and simmer for a few minutes until it thickens a bit. Turn off the heat and add half the cheese. Stir to melt the cheese. Taste and adjust the seasoning with salt and pepper. Cover and keep warm.
In another medium skillet over medium-low heat, add the remaining tablespoon butter. Whisk the eggs well, and sprinkle them with salt and pepper. Pour the eggs into the pan, add the remaining cheese and reduce the heat to low. Cook slowly until the cheese is melted and the eggs are cooked through but soft.
Place the potato pancake on a serving plate. Top with the cheesy eggs and pour on the sauce. Dollop on the caviar and sprinkle over the chives. Cut into 4 slices and serve.