Preheat a large cast iron pan over medium-high heat until hot but not smoking. Add the avocado oil. Season the pork shoulder roast with the sea salt and black pepper, then sear it in the hot pan for 4-5 minutes per side until browned all over. This helps develop flavor and a beautiful crust. I always make sure the pork has a nice golden sear—it really enhances the final taste.
Remove the seared pork roast from the pan and place it at the bottom of a 6-quart slow cooker. In the same pan, add the diced onion and minced garlic. Sauté briefly over medium heat until the onion just begins to soften, about 2-3 minutes.
Turn off the heat and pour the chicken broth into the pan, scraping up any browned bits from the bottom to capture all the flavor. Stir in an extra pinch of salt and pepper, then carefully pour the onion and garlic mixture over the pork in the slow cooker. Arrange the potatoes and carrots around and on top of the roast, then tuck in the herb sprigs for added aroma.
Cover the slow cooker and cook on low for 7-9 hours, or until the pork roast is fall-apart tender and the vegetables are cooked through. I usually let it go for the full 8 hours for perfectly tender results.
Carefully remove the cooked vegetables and discard the sprigs of herbs. Arrange the vegetables in a serving bowl. Transfer the tender pork roast to a platter and, if desired, arrange the vegetables around the pork. Use the cooking juices as is, or make a gravy following your favorite method. To enhance the dish, I sometimes spoon a bit of the flavorful juices over everything just before serving.