In a medium pot, bring potatoes to a boil over high in salted water. Reduce heat and cook at a rapid simmer until potatoes are tender when pierced with a knife, about 20 minutes; drain. Place a folded dish towel on a work surface and place a potato inside. Gently smash potato so that it is flattened but still in one piece (edges will split). Repeat with remaining potatoes.
Preheat oven to 450 degrees. Brush a rimmed baking sheet with 1 tablespoon oil. Place potatoes on sheet and brush tops with 1 tablespoon oil. Bake until crisp and golden, 35 minutes, flipping them halfway through. Remove from oven, toss with vinegar, and season with salt.