Trim the beef brisket of excess fat, leaving about a quarter-inch fat cap to ensure the meat remains moist during the long cook.
In a small bowl, combine the sea salt, black pepper, garlic powder, onion powder, and smoked paprika to create a dry rub.
Apply the dry rub generously to all sides of the brisket, pressing it into the meat to ensure it adheres well.
Preheat your smoker to 225°F using a clean-burning wood like oak or hickory.
Place the brisket on the smoker and cook until the internal temperature reaches approximately 165°F.
During the cook, spritz the meat every hour with apple cider vinegar to keep the exterior hydrated and help develop a deep bark.
Once the brisket reaches 165°F, wrap it tightly in peach butcher paper and return it to the smoker.
Continue cooking until the internal temperature reaches 203°F and the meat feels tender when probed with a thermometer.
Remove the brisket from the smoker and allow it to rest in a room-temperature environment for at least 1 hour before slicing.
While the meat is resting, steam the green beans for 4-5 minutes until they are vibrant and crisp-tender.
Slice the brisket against the grain into thin slices and brush lightly with the sugar-free BBQ sauce before serving with the green beans.