So, like many things in life, there are at least two ways to go about this. The classic way to make this dish is to use firm-ripe yellow plantains, which, in actual appearance, should be turning nice and black on the outside, for the most part. Don't worry, the insides are still perfectly good — they're quite different from bananas.
The other way to do this is to use regular old, ripe bananas. They should be really fragrant and have spots all over. I actually prefer this preparation because that's the way my mom made them when I was growing up — bananas are just much easier to find than plantains here in the States.
Much to my surprise, I was able to find plantains, so I made the dish both ways. So, what's the difference? Well, if you like a chewier texture and a starchy taste, use plantains. They're more appropriate as a side dish and end up looking nicer when deep-fried. (Hence, the plantains are pictured at left.)
On the other hand, if taste matters more to you than appearance, use bananas. Deep-frying them with the light batter transforms the interior into a gooey masterpiece and the crust turns nice and crispy around the edges. For some reason, deep-frying them also brings out a little tang that makes them even more addictive. This ends up tasting more like a breakfast dish, which is the way it's eaten in Indonesia, or with a little ice cream, it can be a great dessert.
Heat the oil in a 2-quart pot to 375 degrees.
In a medium-sized bowl, mix together the tapioca flour, all-purpose flour, water, salt, and sugar to form a loose batter. Line a plate with paper towels for draining. When the oil is ready, dip 3 slices into the batter and carefully slip them in (the batter will make the bananas slippery, so you may want to lower them in using a slotted spoon).
Fry each batch until light golden, about 4-5 minutes. Remove each batch with a slotted spoon to the plate to drain, and dust with cinnamon and powdered sugar, to taste, while still hot. Serve immediately and enjoy.