Preparation

• Combine the flours, sugar, and salt in a bowl. Slowly add the water, stirring to make a smooth, thick batter. Stir in the sesame seeds. Set aside for 30 minutes.
• Peel the bananas. If using large bananas, cut crosswise in half. Cut the pieces or the small bananas lengthwise in half (in either case, you will now have 24 pieces). Set aside.
• Put out a slotted spoon or a spider by your stovetop along with one or two plates. Set a deep-fryer, stable wok, or wide heavy pot over medium heat. Add 2 inches of oil, raise the heat to high, and heat until the oil reaches 360°F. Use a thermometer to check the temperature, or drop a dollop of batter into the oil: If it sinks slowly to the bottom and then rises to the surface, the oil is at temperature. If it bobs right up without sinking or darkens immediately, the oil is too hot—lower the heat slightly; if it doesn’t rise to the surface, the oil is not yet hot enough.
• Stir the batter, then drag 1 piece of banana through the batter and slide it carefully into the hot oil. Repeat with 2 or 3 more pieces, one by one. Fry, moving the pieces around carefully and keeping them from sticking to one another, until lightly golden and crispy. Lift out of the oil with the spider or slotted spoon, pausing to let excess oil drain off, and transfer to a plate. Repeat with the remaining bananas and batter.
• Serve hot, with the lime wedges, sorbet, or ice cream, if you like.