Cut the potatoes into equally-sized pieces. Place the potatoes in a large pot and cover with cold water. Bring to a boil. Add the salt and reduce heat.
Simmer the potatoes for 15 to 20 minutes, or until tender. Drain them.
Leave the potatoes in the pot, and return to the burner, but don't turn the heat on. Allow the potatoes to air dry for a couple of minutes.
Set another large pot over medium heat. Cook the bacon, stirring occasionally, until crispy. Remove bacon from pan and set aside.
To the same pot with the bacon grease, slowly add vinegar, sugar, Dijon mustard, salt, and pepper.
Bring the mixture to a simmer and stir for 2 minutes. Stir the minced garlic into the mixture and cook until lightly golden.
Remove the pot from the heat and toss in the sliced potatoes, gently mixing to combine. Carefully fold in the cooked bacon pieces and chopped parsley.
Transfer the potato salad to a serving dish and serve hot or warm.