Preheat the oven to 180℃/360℉. Grease a loaf pan (mine is a 8×3 -inch loaf pan) or line with baking paper.
Put the soften butter, and sugar in a bowl, whip up with a whisk until it gets pale as it incorporates air bubbles in the batter. Then mix in the greek yogurt.
Add one-third of the egg and keep mixing. Don't add all the egg at once. You need to mix well to emulsify the batter and the egg. When it gets completely incorporated, you can add the other one-third of the egg. Mix them well, and add all of the egg. Then add the vanilla extract as you prefer.
Mix all-purpose flour and baking powder in another bowl, then sift into the batter bowl. Mix with the spatula.
Once it's incorporated, add the mashed banana into the batter. Mix to combine. Don't overmix.
Pour the batter into the prepared loaf pan, bake for 45-60 min depending on your loaf pan size. Insert a toothpick into the center of the cake. Pull it out and it will come out clean when the bread is done.