Preheat the oven to 350 ºF (175 °C). Butter and flour an 8½ x4½-inch (21.5x11.5 cm) loaf pan OR a 9x5-inch (23x12.5 cm) loaf pan, then line the bottom with a rectangle of parchment paper. Set aside.
In a medium bowl, whisk together the flour, baking powder, and salt.
In a large bowl, using an electric hand mixer, cream together the butter and sugar for at least 5 minutes until light and fluffy. Be sure to scrape down the sides of the bowl often to make sure the mixture is evenly whipped.
Add the eggs, one at a time, mixing in between each addition. Mix in the vanilla, if using.
Add the mashed banana. Mix well, scraping the bottom and sides to incorporate everything.
Dump in the flour and fold it in with your spatula.
Pour the batter into the prepared loaf cake pan. Smooth the top to even it out.
Bake for 60–65 minutes for a 9x5" loaf or up to 75 minutes for an 8.5"x4.5" pan, until the edges are a deep golden brown and a cake tester inserted into the middle comes out clean.
Notes
Use the largest bananas you can find for this recipe: I used a pound of bananas and after peeling, I was left with roughly 330 grams of fruit, which works out to 330 mL (1⅓ cups) but this recipe can accommodate up to 375 mL (1½ cups) of mashed banana. Don't use more than that.
Make sure the bananas are very ripe (black even).
If you are using frozen bananas for this recipe, please make sure do the following:
defrost the bananas
peel the bananas and place in a strainer set over a bowl
press very gently to squeeze out the liquid
either discard the banana liquid OR place the liquid in a saucepan and boil it down to a couple tablespoons, stirring often so that it doesn't burn. Add this banana concentrate to the bananas and proceed with recipe.
If you want to make a fancier banana bread, add any of the following:
add 250 mL (1 cup) chocolate chips
add 250 mL (1 cup) chopped walnuts or chopped pecans