Preheat a grill to medium high and prepare for indirect grilling: On a charcoal grill, bank the coals to one side. For a gas grill, turn off half of the burners. Put the onion in a small bowl and cover with cold water; let soak 20 minutes, then drain and squeeze dry. Meanwhile, pulse 1 cup basil, the avocado, garlic, crema and the juice of 1 lime in a blender or mini food processor until smooth; season with salt and pepper. Transfer to a bowl and refrigerate until ready to use.
Tie the beef tenderloin in 2-inch intervals using kitchen twine. Combine 1 tablespoon olive oil, the cumin, 1 teaspoon salt and a few grinds of pepper in a small bowl. Brush the oil mixture all over the beef and transfer to the grill over direct heat. Grill, turning occasionally, until the beef is well marked, about 15 minutes. Transfer the beef to the cooler side of the grill (indirect heat) and continue grilling, turning occasionally, until a thermometer inserted into the center registers 125 degrees F for medium rare, 15 to 20 more minutes. Transfer to a cutting board and let rest 10 minutes.
While the beef is cooking over indirect heat, cut a small slit down the center of each plantain and lightly brush the skins with olive oil; transfer to the grill over direct heat. Grill, turning occasionally, until the skins are charred and the plantains are soft, about 20 minutes; cut into thirds.
Meanwhile, roughly chop the remaining 2 cups basil; toss with the watermelon, the remaining lime juice and 2 tablespoons olive oil, the cheese, aje peppers and onion in a medium bowl. Season with 1/4 teaspoon salt. Slice the beef and serve with the basil crema, plantains and watermelon salad.