Place potatoes in a big pot, cover with water, and boil until soft but not mushy - about 20 to 30 minutes - then drain.
While potatoes boil, place eggs in a pot and fill with enough water to cover them. Bring to a boil, then reduce to simmer for 15 minutes. After simmering, move eggs to an ice bath immediately. Sauté whole kielbasa sausages until brown and crispy. Once browned, remove from pan and cut sausages into semicircles. Return cut sausages to pan and sauté again until browned all over.
Slice potatoes into 1/2" rounds. It's okay if the potatoes fall apart as you slice them, just keep them as together as you can.
Peel eggs and use an egg slicer or knife (egg slicer is easiest) to slice the eggs into rounds.
Grease an 8" x 11" baking dish. Begin placing a third of the potato rounds into the baking dish in a single layer, slightly overlapping each potato slice. Be sure to season the potato layer with salt and pepper before moving to the next layer.
Next, layer half of the sausage on top of the potato layer.
Then spread half the eggs on top of the sausage layer.
Mix sour cream with enough water to make the sour cream more spreadable and creamy. Start with 3 to 5 tablespoons, and add more as needed. Spread half of the sour cream mixture on top of the egg layer.
Repeat the potato layer, seasoning with salt and pepper and leaving a third left for the last layer, then the rest of the sausage, and the rest of the eggs. Spread the remaining sour cream on the egg layer.
Finish the casserole by layering the remaining potato rounds and seasoning with salt and pepper. Top with shredded cheddar cheese.
Bake at 400°F for 30 to 45 minutes, until cheese is melty, bubbly, and golden.