Preheat the oven to 450°F
Score the fat of the pork shoulder with a sharp knife.
In a small bowl, combine the olive oil, salt, thyme and minced garlic. Rub this mixture all over the meat on all sides.
In a large oven-safe skillet or roasting pan, place the onion, celery, and carrots. Place the meat fat side up on top of the vegetables in the pan.
Roast for 30 minutes, until the fat on top is rendered and crisp. Reduce the oven temperature to 350°F.
Roat for 2 to 3 more hours, until the meat is very tender and juicy.
Remove the pan from the oven, cover the meat with tin foil, and let it rest for 10 to 15 minutes. Then remove the cover, slice and enjoy.