Optional garnish of fresh snipped chives, chopped parsley, sliced scallions, sour cream or plain yogurt.
Cook & Grate Potatoes: Fill a large pot halfway with water and bring to a boil. Add potatoes and boil them for 1/2 hour. Remove potatoes from pot and cool them in the fridge for at least two hours or as long as overnight. Once cooled, peel potatoes and grate them into a large bowl using the large holes in a cheese grater.
Saute Onions & Ham: Melt butter in a medium skillet over medium-low heat. Add onions and cook for 5 minutes, until translucent. Add ham and cook, stirring, for 2 minutes. Scrape the mixture into the bowl with the potatoes.
Assemble the Casserole: Preheat oven to 400°F. Add yogurt, mustard, cheese, salt, pepper and cayenne to the bowl with the potatoes, ham and onions. Toss gently to combine (I like using my hands for this) Spread potato mixture evenly into a baking dish (about 13 x 9–inch) coated with cooking spray or lightly oiled. Bake for 25 minutes. Turn the heat up to broil and cook for 4-5 minutes longer, checking every minute, until the top is lightly browned. Turn the heat back down to 400. Remove the casserole from the oven. With the back of a tablespoon, make 8 indentations in top of the casserole. Crack 1 egg into each hole. Return dish to oven. Bake at 400° for 10-12 minutes or until egg whites are firm and yolks barely move when pan is jiggled. Cut into 8 pieces. Garnish with chives, parsley or scallions, sour cream or yogurt, if desired. Serve immediately.
For brunch or lunch, a simple green salad or steamed asparagus would be a good accompaniment.