Boil the potatoes in salted water until tender, 6 to 8 minutes. Remove from the heat and immediately transfer the potatoes to a bowl of ice water to stop the cooking. Cut the cooked potatoes into 1/2-inch thick coins and set aside.
Cut the bacon into 1/2-inch pieces. In a heavy-bottomed saute pan set over medium heat, cook the bacon until crispy, about 4 minutes. Remove the bacon to a paper towel-lined plate and reserve. In the same pan, add the onions and cook until soft, about 2 minutes. Add the garlic and cook until fragrant, about 1 minute more. Stir in the mustard and vinegar and scrape any browned bits from the bottom of the pan into the dressing. Remove from the heat, gently stir in the potatoes and toss to coat. Stir in the parsley and season with salt and pepper. Serve warm.