Melt the butter in a small saucepan over a low heat, taking special care not to let it burn. You will see small white islands of milk solids rising to the top after a couple of minutes. Carefully skim these off and discard. Pour the golden butterfat into a mixing bowl, while at the same time trying to leave any residual white water that lurks below the butterfat in the saucepan.
Peel and shred the potatoes on the larger setting of a grater. Give the gratings a good squeeze to get rid of the initial starchy water (there is no need to strangle them). Add the potato to the butter in the bowl and sift over the flour. Grind in a heavy bombardment of black pepper and then a bit more. Add the salt and use your fingers to mix everything together very thoroughly. If the potato appears to discolour as it oxidises, this is normal, but the aim should be to cook it sooner after grating rather than later.
Heat a large, nonstick frying pan to a medium heat, place all the rosti mixture in the centre of the pan and spread it out to the edge with the back of a spoon. It needs to be pressed flat and spread out really thinly and evenly, but without holes. It will look rather like the inside surface of a fibreglass boat. If you have too much mixture, take a little out, as it should be crispy, not cakey. The rosti should gently sizzle away for about 8–10 minutes on each side. Lift an edge and have a peek; if it is golden brown, flip it over with a big spatula or your fingers (it can be handled fairly robustly, as the starch has glued it together well) and fry the other side. The whole thing can take 16–22 minutes. It wants to be deep orange, browny-gold and very crisp, but with a slight squidge. I regulate the cooking with occasional flipping and heat control.
While your rosti fries, strip the dill feathers from the stalks and roughly chop them, then finely dice the onion. When the rosti is ready, lay it on some baking paper on a plate. Working clockwise around the edge, and in no particular order, dollop the crème fraîche and salmon eggs in separate piles, followed by the dill, onion and lemon wedges. What you do after that is up to you.