Pour 2–3 inches of neutral oil into a deep, heavy pot and heat over medium heat until it reaches 350°F on an instant-read thermometer.
Peel the bananas and slice each one on a diagonal into 3–4 thick pieces, about ¾ inch each.
In a bowl, whisk together the flour, cornstarch, sugar, and salt. Pour in the ice-cold sparkling water all at once and stir just until combined, 5–6 strokes — the batter should stay lumpy.
Working in batches of 3–4 pieces, dip each banana piece in the batter, let excess drip off, and lower gently into the hot oil.
Fry for 2–3 minutes, turning once, until deep golden and crackly. Check the oil temperature between batches and let it recover to 350°F before adding more pieces.
Lift pieces out with a spider strainer and set on a wire rack over a sheet pan. Let drain for 30 seconds.
Serve immediately, plain or with honey, cinnamon-sugar, or a scoop of vanilla ice cream.