Prep the porkshoulder - Score the skin of the pork in a cross hatch pattern, being careful to not cut through to the flesh.
Mise en place - Peel, smash, and coarsely chop the garlic. Rinse the anchovies. Destem and mince the rosemary.
Marinate the pork shoulder - Add the garlic, anchovies, rosemary, salt, and pepper to the bowl of a small food processor, and pulse to combine. Add ¼ cup of olive oil and 2 T mustard to the bowl, and process until it forms a uniform paste, scraping down the sides as needed. Rub the paste all over the pork shoulder, loosely cover it with plastic wrap, and refrigerate it overnight.
THE MORNING OF
Preheat the oven and sear the pork shoulder - Preheat the oven to 450 F and bring the pork to room temperature while the oven preheats. Place the pork in a shallow roasting pan or a large cast iron skillet and roast, uncovered, for 30 minutes, until the top starts to brown a bit.
Slow-roast the pork shoulder - Turn the heat down to 250 F and continue to cook, uncovered, for about 8 hours until the middle of the roast registers not less than 180 F and the meat is very tender throughout. Take the pork shoulder out of the oven and allow it to rest for at least 20 minutes. Pour the juices from the pan into a fat separator.
Slice and serve - After the pork has rested, slice it and arrange it on a serving platter. Garnish the pork with a sprinkling of salt and a drizzle of the defatted pan juices, and serve.