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While the onions are caramelizing, put the potatoes in a large pot of cold, salted water, bring to a boil and cook until nearly tender, but a knife inserted into the centers still meets a little resistance, 10 to 12 minutes, or cooked through. Drain well and smash with the back of a wooden spoon.
Add the potatoes to the onions packing it evenly with the back of a metal spatula to form a cake. Season with the paprika, salt and pepper and cook until the underside is golden brown, about 10 minutes. Invert a plate or baking sheet without sides over the pan and carefully invert the potato cake onto it. Carefully slide the potato cake back into the skillet and cook until the bottom is just set and pale golden brown, about 4 minutes. Spread the cheese on top, cover the pan with a lid and let melt. Transfer the potato cake to a cutting board cheese-side up and cut into wedges. Garnish with chopped fresh chives.