Preheat the grill for two-zone cooking, aiming for a temperature of 250 degrees Fahrenheit.
Remove the membrane from the back of the beef ribs using a butter knife and paper towel.
Mix the brown sugar, smoked paprika, garlic powder, onion powder, salt, and black pepper to create the dry rub.
Apply the dry rub generously to all sides of the beef ribs.
Place the ribs on the indirect heat side of the grill and cook for about 2.5 to 3 hours.
Brush the ribs with barbecue sauce during the last 30 minutes of cooking.
Remove from the grill, let rest for 10 minutes, then slice between the bones and serve.