Preheat the oven to 300℉ (148℃). (Alternatively, use a slow cooker and cover the brisket ¾ of the way with broth or water.)
In a bowl, mix together brown sugar, paprika, salt, black pepper, chili powder, garlic powder, onion powder, and cayenne pepper to make the dry rub.
Pat the beef brisket dry with paper towels. Rub the dry rub all over the brisket, covering all sides. Wrap in foil and place fat side up on a baking sheet. Cook the brisket in the oven for 3 hours (or in the slow cooker for 6–8 hours).
Remove from oven and rest for 30 minutes before slicing against the grain.
Add sliced cucumber to cold water. Chill in the fridge while preparing the meal.
Preheat grill or grill pan to medium heat. Grill the corn on all sides until nicely charred and tender. Lather with butter and season with salt and pepper.
Assemble sandwiches: Portion the sliced brisket onto the bun. Top with barbecue sauce and the top bun.
Serve the sandwich with grilled corn, watermelon, cucumber water and ice cream with sliced banana.