Trim the beef brisket of excess external fat, leaving about a quarter-inch cap to maintain moisture during the long cook.
Combine the smoked paprika, garlic powder, onion powder, sea salt, and black pepper in a small bowl to create the dry rub.
Apply the dry rub generously to all sides of the brisket, pressing it firmly into the meat to ensure it adheres.
Prepare your smoker or oven to 225°F and cook the brisket until the internal temperature reaches 190°F for a tender texture.
In a small saucepan, whisk together the apple cider vinegar, tomato paste, honey, and water over low heat until smooth.
During the final 30 minutes of cooking, brush the BBQ glaze over the exterior of the brisket to create a tacky finish.
While the brisket rests for at least 15 minutes, steam the broccoli florets until tender-crisp and toss with olive oil.
Slice the rested brisket against the grain into thin strips and serve immediately alongside the steamed broccoli.