Preheat the oven to 450°F. Put potatoes and 6 tablespoons of vinegar in a large pot. Fill the pot with enough water to cover the potatoes by 1 inch. Set the pot over high heat and bring to a gentle boil. Boil for 10-15, until the potatoes are just fork-tender. Drain and transfer to a rimmed baking dish.
Smash the potatoes by either placing an additional rimmed baking sheet on top of the potatoes and pressing down. You can also use a skillet, plate, or a mug to smash each potato. Break a few apart to get jagged edges and spread out on the baking sheet.
Toss the potatoes gently with olive oil, the additional tablespoon of vinegar, salt, and pepper and place in the preheated oven. Bake for 20 minutes, tossing halfway through until the potatoes are golden brown. Remove the tray from the oven and sprinkle the grated cheese over the top of the potatoes. Place back in the oven and bake until the cheese is melted, about 5 minutes.
Transfer potatoes to a serving dish and top with chopped cornichons and fresh herbs.
