Place cubed potatoes in a saucepan and cover with salted water. Bring to the stove, over medium high heat, and bring to a boil. Once boiling, reduce the heat to low and simmer until tender, about 10 minutes. Drain the potatoes and transfer to a large bowl. Add 1/2 cup milk and butter, and mash until smooth.
Add the remaining milk, flour, egg, salt, pepper, cheese and chopped chives to the mashed potatoes, stirring to combine.
Preheat a large nonstick skiller, over medium heat. Add the olive oil and, once shimmering, pour about 1/4 cup of the pancake batter, using a spatula to form 3-inch circles. Cook the pancakes (working in batches) until golden brown, about 5 minutes per side. As they cook (and the cheese melts), you might need to gently nudge them with the spatula, encouraging them to keep a round form.
Serve immediately, topped with sour cream and chives.