In a pressure cooker, combine potatoes and water. Cover, set to high, and cook until the potatoes are just underdone. Drain the potatoes, cover, and refrigerate until thoroughly chilled, at least 1 hour. Cut the potatoes into 1/4-inch thick slices. Set aside. (Note: if you don't have a pressure cooker, you can certainly just put the potatoes into boiling water in a large pot on the stove, and cook until just underdone.).
In a large skillet over medium-high heat, cook bacon until crisp, 7 to 10 minutes. Using slotted spoon, transfer bacon to paper towel-lined plate. Reserve bacon fat in the skillet. Let bacon cool, then crumble it into pieces. Set aside.
Transfer 1 tablespoon of bacon fat to a bowl and set aside. Reserve 3 tablespoons bacon fat in the skillet and discard any remaining fat.
Set skillet over medium-high heat and arrange potato slices in the pan in a single layer. Cook, turning potatoes once, until brown and crispy, about 2 minutes per side. Using tongs, transfer potatoes to large bowl.
Whisk the mustard, vinegar, salt, and pepper into the bowl with the 1 tablespoon of reserved bacon fat. Slowly drizzle in the olive oil, whisking constantly. Pour dressing over potatoes. Add the bacon, parsley, green onions, salt, and pepper and stir gently to combine. Serve immediately.