Preheat oven to 350 °F and lightly grease your muffin tin. If you are using frozen bananas, set them near the pre-heating oven to let them defrost enough to peel them.
If you are planning to mix the muffin batter by hand, pre-mash the bananas. If you are going to use a mixer, skip this step.
In a large bowl or the bowl of a mixer, cream together butter and sugar on low (or by hand) until smooth and well blended, about 3 minutes. Mix in the eggs and vanilla until combined.
Next, add in the banana. If you are using a mixer, simply break the banana into a couple pieces each and toss them in. While the banana is getting smooshed, measure in the baking soda and salt. Once the banana is in small pieces and everything looks blended, mix in the flour. Make sure to blend the flour into the batter but don't continue to mix after that happens. If you're using them, fold in the nuts.
Fill your muffin tin to just ⅔ full to avoid a spillover incident. Then, bake muffins for 20 minutes for standard size, or 10 minutes for mini muffins. Poke the center of 2-3 muffins with a toothpick and see if it comes out clean. If not, continue to cook for up to 5 minutes longer.
Allow the muffins to cool for a couple of minutes, then remove them from the tin and let them cool completely. Meanwhile, melt the butter and mix together the cinnamon sugar topping. Dip each muffin into the melted butter, coating either the top or the whole muffin well, then roll the buttered portion around in the cinnamon sugar. Next, stick the muffins directly into your mouth and enjoy.
Muffins store for about 3 days at room temperature but can be frozen, to maintain quality, in an air tight container or bag, for about 3 months.