Preheat oven to 350 degrees F. Use about 2 tablespoons of the olive oil to generously grease the bottom and sides of a loaf pan. It's OK if some pools at the bottom.
In a large bowl, mix the remaining olive oil (just under 1/2 cup) with the brown sugar (1/2 cup).
Add the eggs and mix for about 1 minute.
Add the bananas (see notes) and mix together.
Stir in the baking soda, kosher salt, cinnamon, and vanilla extract (1 teaspoon of each).
Stir in the whole wheat flour (1/2 cup) and the all-purpose flour (1 cup) until just incorporated and no dry spots remain.
Pour batter into prepared loaf pan and bake at 350 degrees for 50-60 minutes, or until toothpick inserted into center comes out clean.
Allow to cool in pan for at least 10 minutes. It should pop right out if you flip the pan upside-down, but if you need to give it a boost you can run a knife along the sides before flipping it over.
Cut the banana bread into 10 slices. I recommend serving it warm with salted butter spread on top.
Baking times can vary based on a number of factors, such as how hot your oven runs, how big the bananas or eggs are, etc. Keep an eye on it and know that it may take a little longer than 60 minutes to fully cook- be sure to insert a toothpick in the center and make sure it comes out clean so you know it's finished.
Storage: Store in an airtight container at room temperature for up to three days or in the refrigerator for up to a week. You can also freeze it (I recommend slicing it first, so you can grab one piece when you want it) in an airtight plastic bag for up to 6 months- squeeze as much air out of it as you can before freezing.
I recommend putting whole, too-ripe bananas in your freezer, unpeeled. When you want to use them for banana bread or other baked goods, take them out and microwave for 1-2 minutes. Then, cut the top of the banana off and squeeze the inside out directly into the mixing bowl. They will be so soft, you don't have to worry about mashing or crushing them beforehand.
Olive oil substitution: You can use butter, or another oil such as canola (which is cheaper) or coconut, in place of the olive oil.
Flour substitution: I don't really recommend using ALL whole wheat flour, as the bread will be dense and dryer, but you can try different ratios between whole wheat/regular flour, or use all white flour if you prefer.
The provided nutrition information does not include any added sodium from seasoning to taste, any optional ingredients, and it does not take brands into account. Feel free to calculate it yourself using this calculator or by adding the recipe to Yummly.