For the rice, heat 1 teaspoon of the oil in small saucepan on medium heat. Add turmeric and cook, stirring, until toasted, about 30 seconds. Add rice and stir to coat. Add water and salt. Bring to a boil. Reduce to a low simmer; cover and cook 15 minutes or until all of the water has been absorbed and rice is tender. Remove from heat and stir in mayonnaise and garlic. Season to taste with salt and let cool completely. Set aside.
Prepare grill for indirect medium heat. For gas grills (with 3 or more burners), turn all burners to medium-high heat; after about 15 minutes, turn off one of the side burners and turn the remaining burners down to medium. For charcoal grills, bank one chimney starter-full of lit and ashed-over charcoal briquettes to one side of the grill. Set up a drip pan on the other side to avoid flare-ups. (Be sure to consult the grill manufacturer's guide for best results.) If your grill has a thermometer, aim to keep the temperature at about 350°F throughout grilling.
For the peppers and plantains, heat 2 tablespoons of the oil in a medium flameproof skillet over the direct-heat side of grill until hot and shimmering. Add peppers and cook about 5 minutes until softened; set aside. Add plantain halves cut-side down and cook, flipping once, until golden and caramelized; about 5 minutes per side. Let cool, then cut one of the plantain pieces in half lengthwise to make 3 strips total. Set aside.
For the beans, place beans and 2 tablespoons of the Bar-B-Q Sauce in small bowl. Add a pinch of salt and squish the beans with your hands until broken down enough to hold together but not completely a paste. Set aside.
For the flank steak, place steak on cutting board with short end facing you. Starting at one long side, slice the steak in half horizontally, leaving 2 inches at the opposite long side uncut so the top and bottom of the steak stay attached. Open steak like a book so you have 1 large piece. Pound steak with a meat mallet to an even thickness of about 1/2 inch. Sprinkle both sides of the steak with the Seasoning.
Position the steak vertically in front of you so the short ends are at the top and bottom of the cutting board. Pat rice into an even layer all over the steak. Starting 1/3 of the way in from the left side of the steak, lay down one plantain strip vertically on the steak. Moving right, line up 4 scallions next to it, followed by 1/3 of the peppers and 1/3 of the beans. Repeat 2 times with remaining ingredients, starting with a plantain strip and ending with beans. Starting at one of the long ends, roll steak around the filling like a jelly roll. Tie closed at 1-inch intervals around the circumference with kitchen twine. Tie 1 more piece of twine lengthwise around the meat to secure. Brush steak evenly with remaining 1 tablespoon oil.
Lightly brush grill grates with oil. Grill steak on direct-heat side of grill to brown all 4 sides; about 10 minutes total. Move steak to indirect-heat side of grill; close grill. Grill 30 minutes, turning occasionally, until center registers 115°F on a thermometer for a steak that is well done on the outside and medium rare in the center. Baste with remaining 1/4 cup Bar-B-Q Sauce during the last 5 minutes of grilling; Transfer steak to cutting board and let rest 15 minutes.
Untie steak and slice on a slight bias into 6 thick slices. Serve with more Bar-B-Q Sauce on the side.