Put the potatoes and 1 teaspoon salt into a medium saucepan and add water to cover by about 1/2 inch. Cover and bring to a boil over high heat. Uncover, reduce heat to prevent a boilover, and boil until the potatoes are tender when pierced with a fork, 20 to 25 minutes.

Drain the potatoes and pass them through a ricer or food mill back into the saucepan (or mash them as smoothly as possible with a hand masher). Add the cheese, 3 tablespoons of the olive oil, the sour cream, pepper, and 1/2 teaspoon salt; mix thoroughly. Add the chives and stir until well mixed. Taste and add more salt and pepper, if necessary. Divide the potato mixture into quarters and shape each into a squat patty about 3/4 inch thick. (If making ahead, put the patties on a plate or tray in a single layer, cover with plastic, and refrigerate.)

Heat the remaining 2 tablespoons oil in a 10-inch nonstick pan over medium-high heat. When the oil is hot, set the cakes in the pan so they aren't touching. Cook until a deep brown crust forms, 2 to 3 minutes, and then turn and brown on the other side, another 2 to 3 minutes (the cooking time will be a bit longer if the patties are chilled). Serve immediately, topped with a dab of sour cream and a sprinkle of chives.