Preheat a large cast iron pan over medium-high heat until hot but not smoking. Rub the pork shoulder roast all over with olive oil, then sprinkle with sea salt and freshly ground black pepper. Sear the roast in the hot pan for 4-5 minutes per side until golden brown and caramelized.

Remove the seared pork shoulder from the pan and carefully transfer it to the bottom of a 6-quart slow cooker, keeping as much of the flavorful seared exterior intact as possible.

Add the diced white onion and minced garlic to the same cast iron pan used for searing the pork. Sauté briefly over medium heat until the onion just begins to soften, about 2-3 minutes. I find this step really helps to build a deep, savory flavor base for the final dish.

Turn off the heat and add the chicken broth to the sautéed onion and garlic in the pan. Use a wooden spoon to scrape up any browned bits stuck to the bottom of the pan. Stir in the remaining salt and pepper until they dissolve completely.

Pour the onion, garlic, and broth mixture over the pork shoulder in the slow cooker, making sure the roast is evenly surrounded. Arrange the potatoes and carrots around and on top of the pork. Tuck the fresh herb sprigs throughout the slow cooker, nestling them among the vegetables. Cover and cook on low for 7-9 hours, until the pork is very tender and the vegetables are cooked through. Personally, I like to cook mine for a full 8 hours to ensure the roast is falling-apart tender.

Carefully remove the cooked vegetables and herbs from the slow cooker. Discard the herb sprigs and transfer the vegetables to a serving bowl. Next, gently lift the tender pork roast onto a serving platter and arrange the vegetables around it. Use the flavorful juices in the slow cooker to serve alongside or turn them into a quick gravy if you like.