In a large bowl, mash the bananas. It's fine if the mashed bananas have a few small lumps in them.
Add the eggs, vegetable oil, and vanilla extract and stir to combine. Then add the white granulated sugar and whisk to combine.
In another bowl, whisk together the all purpose (plain) flour, baking powder, baking soda (bicarbonate of soda) and salt.
Add the flour mixture to the bowl with the banana mixture and mix lightly with a spoon or spatula until combined.
Fill each paper liner just halfway with the batter. This will ensure that the cupcakes rise and bake evenly with a level top, avoiding any doming.
Bake for 15 to 18 minutes until the centers are springy to the touch and the tops are golden brown. Rotate the pan halfway through for even baking.
Let the cupcakes cool in the pan for a few minutes, then remove and place on a wire rack to cool completely.