In a large saucepan of simmering salted water, cook the potatoes until tender, 30 to 35 minutes. Drain and set aside.
Meanwhile, in a large nonreactive skillet, cook the bacon over medium heat until crisp, about 10 minutes. Reserving the fat, drain the bacon and set aside.
In the bacon fat, saute the onion over medium heat until softened but not browned, about 10 minutes. Stir in the flour, sugar, dry mustard, salt, celery seed, and black pepper. Reduce the heat to low and cook, stirring constantly, until the mixture has slightly thickened, about 5 minutes.
Remove the skillet from the heat and stir in the water and vinegar. Bring the dressing to a boil, stirring constantly, and cook for 1 minute. Remove from the heat.
Add the reserved crumbled bacon to the hot dressing. Slice the unpeeled potatoes into the dressing and stir gently to coat them. Return the skillet to medium heat and cook, stirring gently, until the dressing is hot and bubbly, about 1 minute.
Transfer the hot potatoes to a large serving bowl. Stir in the eggs, green pepper, celery, and parsley. Serve salad warm.