Combine smoked paprika, paprika, cumin, mustard powder, coriander, 2 tsp brown sugar, garlic powder, and salt in a small bowl to create your dry rub. Trim the brisket to a uniform 1/4-inch fat cap on all sides—this helps the meat cook evenly and absorb the spice flavors. Rub the mixture generously all over the meat, working it into every crevice. Roll the brisket tightly and tie it with kitchen string at 2-inch intervals to maintain an even shape during the long braise.
Preheat your oven to 160°C (320°F). Place the tied brisket in a braising dish or Dutch oven and pour the beef stock around it. Cover tightly with foil or a lid and braise for 4 hours. After 2 hours, carefully open the dish and baste the meat with the cooking liquid, adding a little water if the liquid has reduced too much. The meat should be nearly falling apart when pierced with a fork—if it still feels firm after 4 hours, give it another 30 minutes.
While the brisket braises, prepare the sauce that will finish the dish. In a small saucepan, combine rum, ketchup, red wine, balsamic vinegar, Worcestershire sauce, and 2 tbsp brown sugar. Heat over medium heat and stir occasionally for about 2 minutes to warm through and marry the flavors. In a small cup, mix gravy powder with 2 tbsp water until smooth, then add it to the pan and stir constantly for 1-2 minutes until the sauce thickens to a glossy consistency. I like to taste the sauce here and adjust with a pinch more salt or vinegar if needed—it should be rich and slightly tangy.
Start the rice according to package directions—this will take about 15-20 minutes and can cook while the brisket finishes braising. In a separate bowl, combine shredded cabbage, grated carrot, mayonnaise, and Dijon mustard, mixing well so the vegetables are evenly coated. I prefer to make the slaw at least 15 minutes before assembly so the cabbage softens slightly and the flavors meld together, but it can be made earlier if needed.
Once the brisket is fork-tender and easily shreds, remove it from the braising liquid and let it rest for 5 minutes. Using two forks or your hands, shred the meat into bite-sized pieces, discarding any excess fat or string. Gently stir the shredded brisket into the warm sauce from Step 3, coating every piece evenly. This keeps the meat moist and infuses it with that rich, slightly sweet and tangy flavor that defines great brisket burritos.
Heat a dry skillet over medium heat and warm each tortilla for about 15 seconds per side until pliable—this makes them easier to fold without tearing. Alternatively, you can stack them and warm them together in a microwave for 30 seconds. Lay a warm tortilla on a flat surface and add a portion of rice down the center, followed by a generous scoop of shredded brisket with sauce, then a handful of cabbage slaw. Fold in the sides and roll tightly away from you. Sprinkle fresh parsley over the top and serve immediately while everything is warm.