Preheat your oven to 350°F (180°C) and grease a 9x5 inch loaf pan or line it with parchment paper.
Peel the ripe bananas and mash them thoroughly in a large bowl until smooth, with some slight lumps for texture.
Add the oil or melted butter, brown sugar, and vanilla extract to the mashed bananas. Mix with a spatula until the mixture is well combined and slightly fluffy.
In a separate bowl, whisk together the rolled oats, flour, baking powder, and salt.
Gradually add the dry ingredients to the banana mixture, folding gently with a spatula until just combined. Be careful not to overmix.
If the batter feels very thick, stir in a splash of milk or water to loosen it slightly, aiming for a scoopable but not runny consistency.
Pour the batter into the prepared loaf pan, smoothing the top with the spatula until even.
Bake in the preheated oven for 45-50 minutes, or until the top is golden brown and a toothpick inserted into the center comes out clean.
If the top darkens too quickly, tent the loaf with foil and continue baking. Check doneness with a toothpick near the end of baking time.
Remove the bread from the oven and let it cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.
Slice the cooled bread with a serrated knife, and enjoy it warm or at room temperature for a cozy treat.