Put the potatoes in a large saucepan, cover with cold water and season generously with salt. Bring to a boil, reduce to a simmer and cook until the potatoes are tender, 15 to 20 minutes. Drain and let cool slightly. Gently smash with a fork or potato masher.
Meanwhile, in a large bowl, whisk together the oil, parsley, mustard, vinegar, shallots and jalapeno. Season with salt and pepper. Add the potatoes and gently combine. Serve at room temperature.