Season pork shoulder roast generously with sea salt and black pepper.
Heat olive oil in a 4-quart oven-safe pot with a lid over high heat. Sear seasoned pork roast in hot oil on all sides until completely browned, 2 to 3 minutes per side. Remove the pork roast to a cutting board, reserving the fat in the pot.
Allow the pot to cool slightly and place over low heat. Cook and stir onion and garlic in reserved hot oil until the onions are translucent, about 5 minutes. Pour the chicken broth into the pot; bring to a boil while scraping the browned bits of food off of the bottom of the pan with a flat-edged wooden spoon. Stir liquid smoke into the onion mixture. Return pork roast to the pot and cover with a lid.
Bake in preheated oven until completely tender, 3 to 4 hours.
Remove pork to a cutting board, cover loosely with aluminum foil, and allow it to rest for 15 minutes. Shred the pork with a 2 forks into fine shreds. Return shredded pork to the pot and stir with the remaining liquid to serve.
