Cut the peeled potatoes into large chunks and place in a pot of salted water; bring to a boil and cook until the potatoes are tender when pierced, about 15–20 minutes.
Drain the potatoes well, then pass them through a ricer or mash until very smooth; transfer to a mixing bowl.
Stir in the grated Gruyère, 6 tablespoons olive oil, 6 tablespoons sour cream, and 1–2 tablespoons chopped chives; season with salt and pepper to taste until evenly combined.
Portion the mixture into patties using about 1/4 cup per cake, shaping them gently so they hold together.
Heat a thin layer of olive oil in a skillet over medium heat. Fry the patties until golden brown on the first side, about 3–4 minutes, then carefully flip and cook until the second side is golden and heated through.
Serve the potato cakes topped with a dollop of sour cream (or crème fraîche) and a sprinkle of chives; for an appetizer option, add smoked salmon and a sprig of dill if desired.