Preheat the oven to 350 degrees(F).
In a large mixing bowl, sift together the flour, baking soda, cinnamon, and then stir in the salt.
In a separate large mixing bowl, or the bowl of a stand mixer, beat together the sugar and butter. Either with a hand mixer or the paddle attachment of the stand mixer.
Add the applesauce to the butter and sugar, and beat until combined, scraping down the sides of the bowl as needed.
Add the mashed bananas, yogurt, and vanilla to the wet ingredients. Beat again until combined.
Now, add the dry ingredients to the wet about 1/2 cup at a time, beating together, until everything has been fully incorporated. Set aside.
Now mix the cinnamon swirl ingredients. Whisk together the cane sugar, cinnamon, and nutmeg in a small mixing bowl. Set aside.
Pour half of the banana bread batter into a 9-inch loaf pan lined with parchment paper, spread it out evenly.
Sprinkle the cinnamon swirl mix over the top evenly. Then pour the remaining batter over the cinnamon and sugar and smooth it out evenly.
Bake for 55-65 minutes, or until a toothpick comes out clean from the center of the bread.
Let cool for a few minutes, slice, and serve with vegan butter if desired.