Put the sweet potatoes in a large saucepan and cover with 2 inches water. Add 2 tablespoons salt. Bring to a gentle simmer and cook until the sweet potatoes are knife-tender, 10 to 15 minutes. Drain well and put in a large bowl. Keep warm.
Meanwhile, cook the bacon in a large nonstick skillet over medium heat until crisp, 8 to 10 minutes. Remove the bacon from the grease and set aside on a paper towel-lined plate, leaving the grease behind in the skillet. Return the skillet to medium-low heat, then add the onions and cook until translucent, about 10 minutes.
Stir the mustard and vinegar into the skillet with the onions, then whisk to combine. Let the dressing simmer for a minute, then pour over the sweet potatoes in the bowl. Add half of the bacon and toss to coat evenly. Season with salt and pepper.
Transfer the sweet potato salad to a serving platter and garnish with the remaining bacon and parsley. Serve hot or chill to serve cold.