Preheat the oven to 350°F (175°C). Grease and flour an 8-inch round cake pan.
In a large bowl, mash the ripe bananas with a fork until smooth.
Add the eggs, vegetable oil, and vanilla extract to the mashed bananas. Mix well until combined.
In a separate bowl, whisk together the all-purpose flour, baking soda, baking powder, salt, and ground cinnamon.
Gradually add the dry ingredients to the wet ingredients, stirring gently until just combined.
Fold in the plain Greek yogurt until the batter is smooth.
Pour the batter into the prepared cake pan and spread it evenly.
Bake for 40 to 45 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and let it cool in the pan for 10 minutes.
Transfer the cake to a wire rack to cool completely before serving.