Heat the vegetable oil in your large pan over medium heat until it shimmers slightly but doesn't smoke. This usually takes about 3-4 minutes.
Carefully add the peeled bananas to the hot oil one at a time, placing them gently to avoid splashing. The oil should sizzle around each banana when added.
Fry the bananas for approximately 3 minutes without moving them, allowing the bottom side to develop a light golden color and slight firmness.
Sprinkle the brown sugar evenly over the bananas and oil. Do not stir at this point - let the sugar sit undisturbed so it can begin melting and caramelizing.
Watch for the sugar to start bubbling and turning amber colored, which typically takes 1-2 minutes. This is when the caramelization process begins.
Once the sugar starts caramelizing, gently stir and turn the bananas using tongs, ensuring each banana gets coated with the caramelized sugar mixture.
Continue frying for another 3-4 minutes, turning the bananas occasionally to achieve even caramelization on all sides. The bananas should be golden brown and glossy.
Turn off the heat when the bananas are beautifully caramelized and cooked through. They should feel tender when gently pressed but still hold their shape.
Transfer the bananas to paper towels or banana leaves to drain excess oil. Let them cool for just 2-3 minutes - they should still be warm for serving.
Carefully thread 2 bananas onto each bamboo skewer while they're still slightly warm and pliable. Serve immediately while hot for the best texture and flavor.