Preheat the oven to 350°F (175°C). Grease a 9×5 inch loaf pan or line it with parchment paper.
In a large bowl, mash the ripe bananas with a fork until smooth.
Add the eggs, granulated sugar, brown sugar, vegetable oil, and vanilla extract to the mashed bananas. Mix well until combined.
In a separate bowl, whisk together the all-purpose flour, rolled oats, baking soda, baking powder, ground cinnamon, and salt.
Gradually add the dry ingredients to the wet ingredients, stirring gently until just combined. Do not overmix.
Pour the batter into the prepared loaf pan and spread it evenly.
Bake in the preheated oven for 55 to 60 minutes, or until a toothpick inserted into the center comes out clean.
Remove the banana bread from the oven and let it cool in the pan for 10 minutes.
Transfer the bread to a wire rack to cool completely before slicing.