Boil 2 baby red potatoes (1-½ to 2 inches in diameter) until tender, about 30 minutes. Heat the oven to 450°F. Drain potatoes on paper towels and, using another layer of paper towels, gently press down on the potatoes with the palm of your hand to flatten to ½ inch. Feel free to say something like, "Yeah, take that, potato!" Place potatoes on a baking sheet, coat each one with 1 tablespoon olive oil and season with salt. Roast the potatoes until crispy and deep brown around the edges, about 30 minutes, flipping halfway through.
Heat a skillet over medium-low and make two small piles of parmesan cheese on the surface. Place a smashed potato on each pile. Top both with cheddar cheese. Cook until cheddar is melted and parmesan is golden brown and crusty. Top one potato with the other, cheese facing in, and smash them together with a spatula. Serve hot with sour cream and chopped chives.