Place the potatoes in a pot with water to cover and 1 teaspoon salt and simmer until tender, 15 to 18 minutes. Drain and run under cold water to cool. Cut into quarters.
Meanwhile, cook the bacon in a skillet over medium-high heat until crisp, 6 to 8 minutes. Transfer to paper towels. Crumble when cool.
In a large bowl, whisk the oil, vinegar, mustard, 3/4 teaspoon salt, and 1/4 teaspoon pepper. Toss with the potatoes, bacon, and parsley.