Cut the bulbs of garlic in half crosswise into a top and bottom. Place the garlic halves on a sheet of foil, drizzle with olive oil and sprinkle with salt. Fold the foil up and around the garlic halves, making sure they stay flat. Seal the foil into an airtight package. Roast until golden and soft, about 60 minutes. Keep the garlic in the foil and let cool slightly.
For the pork:
Place the pork loin in a medium, heavy roasting pan. Season all sides with salt and pepper. Place the pork in the oven 30 minutes after the garlic has started roasting. Roast until an instant-read thermometer registers 140 to 145 degrees F, about 30 to 40 minutes. Remove the roasting pan from the oven, tent the pork loin with foil, and let rest for 15 minutes.
For the vinaigrette:
Remove the garlic from the foil. Remove the cloves by squeezing the base of the garlic. Place the garlic, parsley, and balsamic vinegar in a blender. Pulse the machine until blended. Drizzle the oil into the blender while the machine is running. Add the sugar, salt, pepper, and water and blend until incorporated.
Slice the pork into 3/4-inch thick slices and transfer to a serving platter. Drizzle some of the vinaigrette over the pork and pass the remaining vinaigrette alongside the pork in a small dish.