Preheat the oven to 325°F (163°C).
Prepare the seasoning mix. In a small bowl, mix together the brown sugar, smoked paprika (if using), garlic powder, onion powder, salt, and black pepper.
Prepare the pork shoulder. Trim the pork shoulder of any thick layers of fat and pat the pork shoulder dry with paper towels. Rub the pork with the spice mixture, making sure to cover the sides and crevices.
Rest for 30 minutes.
Sear the pork shoulder. Heat the olive oil in a large Dutch oven set over medium-high heat. Sear the pork on all sides, about 3-4 minutes per side, until a golden-brown. Remove the pork to a clean plate and set aside.
Sauté the aromatics and deglaze the pot. Reduce the heat to medium. Add the sliced onion and minced garlic to the pot, stirring frequently. Sauté for about 4-5 minutes, or until the onions become translucent and the garlic is fragrant, being careful not to burn the garlic. Use a wooden spoon or spatula to scrape up the browned bits from the bottom of the pot—this is called deglazing, and it’s essential for building deep flavor.
Next, slowly pour in the beer and apple cider, stirring as you go. The liquid will bubble up and help loosen any remaining brown bits. Let the mixture come to a gentle simmer, then reduce the heat to low.
Add the pork and herbs. Nestle the seared pork shoulder back into the pot. Tuck fresh thyme and rosemary sprigs on each side of the meat, partially submerging them in the liquid.
Braise in the oven. Cover the Dutch oven with a lid. Transfer it to the preheated oven and braise for 3½ to 4 hours, basting every hour. The pork is done when it’s fork-tender and easily pulls apart.
Rest and shred: Remove the pork from the pot and let it rest for 10-15 minutes. Shred the meat using two forks or slice it as desired.
Strain and simmer the braising juices. Strain the braising liquid into a saucepan. Simmer gently until it's reduced to your preference. Serve the pork with the juices and cooked onions over buttery mashed potatoes, roasted vegetables, or warm crusty bread.