Make the Potato Filling:
Place peeled potatoes in a pot and add enough water to cover them. Bring to a boil over medium-high heat and cook for 25 minutes, or until fork-tender. Drain the potatoes and let them cool for 5 minutes. Mash the potatoes until smooth, then mix in salt, melted butter, cream cheese, and shredded mozzarella. Partially cover and set aside.

Prepare the Pierogi Dough:
In a stand mixer bowl (or large mixing bowl), whisk together warm water, milk, sour cream, egg, oil, and salt. Using a dough hook (or a wooden spoon if mixing by hand), add 2 cups of flour and mix until incorporated. Gradually add the remaining flour ½ cup at a time, mixing well after each addition. Add flour 1 tablespoon at a time until the dough no longer sticks to the sides of the bowl or hands. Knead the dough for 2-3 minutes until smooth and elastic. Cover with plastic wrap and let rest for 30 minutes.

Shape the Pierogi:
Divide the dough into two pieces. Keep one piece covered while rolling out the other on a floured surface to about ⅛-inch thickness. Use a 3-inch round cookie cutter to cut dough circles as close together as possible. Place ½ tablespoon of potato filling in the center of each round. Fold the dough over the filling and pinch the edges tightly to seal. For extra security, crimp the edges with a pinch-and-twist motion. Repeat with the remaining dough and filling. Keep the shaped pierogi covered to prevent drying.

Make the Ground Beef Topping:
Before cooking the pierogi, sauté the ground beef in a medium skillet over medium heat until browned and cooked through. Melt in butter and remove from heat. Set aside.

Cook the Pierogi:
Bring a large pot of water to a rolling boil and add 1 tablespoon of salt. Add the fresh or frozen pierogi in batches. Cook for about 2 minutes, or until the pierogi float to the top and the water returns to a boil. Remove the pierogi with a slotted spoon and place them in a bowl, drizzling with the buttery ground beef mixture between layers to prevent sticking.

Serve:
Serve warm with sour cream on the side. Enjoy!