Arrange the potatoes in a single layer on a baking sheet and roast them until tender when pierced with the tip of a knife, 35 to 40 minutes.
In a bowl that is large enough to hold the potatoes, whisk together the sherry vinegar, mustard, capers and brine, and cornichons and brine. Whisk in the olive oil. Taste for seasoning.
Heat the canola oil in a medium skillet over medium heat. When it is hot, add the rosemary sprigs. They should bubble and froth slightly. Allow the rosemary to cook until its green color pales slightly and the needles become crispy, 2 to 3 minutes. Use a slotted spoon to remove them carefully from the oil and put them on a kitchen towel to drain. Season them with 1 teaspoon of the salt.
Halve the warm potatoes and add them to the bowl containing the dressing. As you mix, lightly crush them with the tines of a fork. Season with the remaining 2 teaspoons of salt. Flake the crispy rosemary needles from the stems over the potatoes. Discard the stems. Serve immediately.
Since the canola oil does not get super-hot to crisp the rosemary, you can reserve it for another use.