To prepare the rösti, start by placing the potatoes in a large pot filled with plenty of cold water. Bring to a boil and cook for about 10–15 minutes; the exact time depends on the size of the potatoes, but they should remain very firm (al dente). Once drained, peel the potatoes and coarsely grate them into a large bowl using a grater with large holes; make sure the potatoes are cool or lukewarm before grating.
Season the grated potatoes with salt and black pepper, then mix thoroughly. Take a 22 cm (9-inch) non-stick skillet, add a portion of the butter (or oil) from the total amount, and let it melt.
Add the grated potatoes to the skillet and cook, stirring, for about 5 minutes over medium-high heat, starting to press and shape the rösti with a spatula.
Add small pats of butter around the edges of the rösti and continue cooking for 6–7 minutes without stirring. Lightly grease a large, flat lid with butter and place it over the pan to carefully flip the rösti.
Melt another small piece of butter in the skillet before sliding the rösti back in. Add a few more pats of butter around the sides and cook the second side for another 6–7 minutes, maintaining medium-high heat. Once the potato rösti is golden and crisp on the outside and tender on the inside, it is ready to be served.