Make a shallow, long cut in the skin of the potatoes and boil them for about 30 minutes, then rinse them with cold water – this makes it easier to remove the skin.
Mash the peeled potatoes and add the butter, corn starch, salt, and pepper, mixing everything until combined. Spoon half of the mash into a casserole dish.
Put 3 slices of ham on top and sprinkle with the shredded cheese.
Add the other half of the mashed potatoes to the dish and smooth it out. With a wooden spoon, draw a few lines in the mash about 1 inch deep, creating 6 rectangles of equal size.
Use a shot glass to press 6 wells into the potato mixture.
Place 2 wooden skewers next to each other and a hot dog between them, cut the hot dog up as far as the knife goes and then shape it into a circle. Use a toothpick to secure the ends of the hot dog.
Repeat the same process with the other hot dogs and place them around the wells in the mashed potatoes.
Mix the heavy cream, chopped dill, salt, pepper, and flour, then pour the mixture into the grooves in the potato mass.
Crack an egg into each hot dog circle and sprinkle more shredded cheese all around before sliding the casserole dish into a preheated oven set to 350°F for 25 minutes.
