Mix the mayonnaise, hot sauce, garlic and paprika in a bowl; cover and refrigerate until ready to serve.
Put the potatoes in a medium pot and cover with cold water by 1 inch; add the vinegar. Bring to a boil, then reduce the heat to medium and simmer until fork-tender, 5 minutes. Drain and transfer to a paper towel-lined baking sheet to dry.
Heat about 1/4 inch of peanut oil in a large cast-iron skillet over medium-high heat until hot but not smoking. Add half of the potatoes and fry, turning occasionally, until golden brown and crisp, about 10 minutes. Remove with a slotted spoon and transfer to fresh paper towels to drain; season generously with salt. Repeat with the remaining potatoes.
Transfer the potatoes to a platter and top with the prepared sauce, blue cheese and parsley. Sprinkle with more paprika.