Preheat the oven to 350°F (175°C). Line a 12-cup muffin tin with paper liners or grease the cups.
In a large mixing bowl, combine the mashed bananas, drained cottage cheese, eggs, sugar, melted butter, and vanilla extract. Mix well until smooth.
In a separate bowl, whisk together the flour, baking powder, baking soda, salt, and ground cinnamon.
Gradually add the dry ingredients to the wet ingredients, stirring gently until just combined. Do not overmix; the batter should be slightly lumpy.
Divide the batter evenly among the prepared muffin cups, filling each about 3/4 full.
Bake in the preheated oven for 18-20 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Remove the muffins from the oven and allow them to cool in the pan for 5 minutes. Then transfer to a wire rack to cool completely before serving.