Preheat your oven to 300°F.
In a small bowl, combine the smoked paprika, garlic powder, onion powder, sea salt, and black pepper to create a dry rub.
Coat the beef brisket evenly with the dry rub on all sides.
Place the brisket in a baking dish, cover tightly with aluminum foil, and roast for 3 hours until the meat is tender enough to pull apart.
While the meat rests, whisk together the tomato paste, apple cider vinegar, and liquid smoke to create a clean-eating BBQ glaze.
Increase the oven temperature to 400°F.
Toss the broccoli florets and sliced carrots with olive oil and a pinch of salt, then spread them on a parchment-lined baking sheet.
Roast the vegetables for 15 to 20 minutes until they are tender and slightly charred.
Brush the BBQ glaze onto the brisket and broil for 2 to 3 minutes until the glaze is bubbly and caramelized.
Slice the brisket against the grain and serve immediately with the roasted vegetables.