Preheat oven to 375 F degrees.
Lightly greasy a 13x9 inch baking dish with oil.
Use a food processor to prepare a smooth mixture from the cheese and butter, and season with ½ teaspoon pepper and salt.
Slice the potatoes on a cutting board and fill one layer with the potatoes in the lightly greased pan. Pour the ⅓ of the cheese mixture on top.
Repeat with the process two more times until you use all the potatoes and cheese mixture.
Cover the pan tightly aluminum foil and bake for about 1 ½ hours or until the potatoes are tender.
Crack the eggs into a medium bowl, and whisk together with the yogurt and ¼ teaspoon of pepper.
Pour over the dish with potatoes and put it back in the oven but this time uncovered. Bake for about 20 minutes or until top is golden.
Before serving, let cool first.