Make the dough: in a large bowl combine the All-Purpose Flour with a pinch of Salt, crack in the Egg and add lukewarm Water a little at a time; mix until a soft dough forms, then knead on a lightly floured surface until smooth. Cover and let rest for 20–30 minutes.
Prepare the potatoes: cook the Starchy Potatoes in boiling water until very tender, drain well and mash roughly while still hot; stir in a knob of Unsalted Butter and adjust seasoning with salt and freshly ground Black Pepper.
Caramelize the filling onion: finely chop the Onion and sauté it in a little more Unsalted Butter over medium heat until golden and sweet; fold the onion into the mashed potatoes and taste, adding more salt or pepper if needed.
Shape the dumplings: roll the rested dough to about 1/8 inch (3 mm) thickness and cut into rounds (about 2–3 inches / 5–7 cm across). Place a spoonful of the potato-onion filling in the center of each round, fold and pinch the edges firmly to seal.
Cook the varenya: bring a large pot of water to a rolling boil and season with salt. Drop the dumplings in batches so they don’t stick, stirring gently; they are done when they float and are cooked through, about 3–4 minutes after rising to the surface.
Finish and serve: remove dumplings with a slotted spoon, transfer to plates and dress with extra melted Unsalted Butter and a generous dollop of Sour Cream. Sprinkle with chopped Dill and serve hot.
