Prepare Potatoes: Begin by peeling the potatoes. Grate them using the largest side of a box grater. Squeeze the grated potatoes as hard as you can to remove any excess moisture, then transfer them to a bowl.
Season and Fry: Season the grated potatoes with salt and pepper, mixing well to ensure even distribution. Heat the ghee in a small frying pan. Press the seasoned potatoes into the pan, forming a compact layer. Fry over medium-high heat for 4-5 minutes, or until the underside is golden brown.
Bake: Carefully flip the rösti in the pan. After flipping, transfer the pan to an oven preheated to 350°F (180°C) and bake for 10 minutes.
Garnish and Serve: Remove from the oven and garnish with smoked salmon and chopped chives. Add dollops of mascarpone on top. Poached eggs also go great with it.