Prep the pan and oven. Heat your oven to 350°F (175°C). Lightly grease a 9x5-inch loaf pan or line it with parchment for easy removal.
Mash the bananas. In a large bowl, peel and mash the bananas until mostly smooth with a few small lumps.
You should end up with about 1 1/4 to 1 1/2 cups of mashed banana.
Whisk in the eggs and sugar. Add the eggs and sugar to the mashed bananas. Whisk until well combined and slightly frothy. If using vanilla or a pinch of cinnamon, stir them in now.
Add the flour. Sprinkle the self-rising flour over the wet mixture.
Use a spatula to gently fold it in until just combined. Stop mixing as soon as no dry streaks remain. If adding chocolate chips or nuts, fold them in now.
Fill the pan. Pour the batter into the prepared loaf pan and smooth the top.
If you like, sprinkle a little sugar on top for a light, crackly crust.
Bake. Bake for 50–60 minutes, or until the top is golden and a toothpick inserted in the center comes out mostly clean with a few moist crumbs. If the top browns too fast, tent it loosely with foil for the last 10–15 minutes.
Cool. Let the loaf cool in the pan for 10–15 minutes, then lift it out and cool on a rack. Slice when it’s just warm or fully cooled for cleaner cuts.