Preheat the oven to 350°F (175°C). Line a 12-cup muffin tin with paper liners or grease the cups lightly.
In a large mixing bowl, combine the mashed bananas, cottage cheese, eggs, vegetable oil, granulated sugar, brown sugar, and vanilla extract. Mix well until smooth.
In a separate bowl, whisk together the all-purpose flour, baking powder, baking soda, salt, and ground cinnamon.
Gradually add the dry ingredients to the wet ingredients, stirring gently just until combined. Do not overmix; the batter should be slightly lumpy.
Divide the batter evenly among the 12 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.