Preheat your oven to 350 degrees, and generously grease an 8 inch loaf pan. You can also line it with parchment paper to make it easier to remove from the pan.
In a large bowl, beat together the sugar and softened butter until fluffy. Add in the eggs, vanilla extract, and applesauce and beat until just combined. Add the flour, baking soda, and salt, and beat together until a batter comes together- it should be fairly thick.
Pour about 1/4 of the batter into a small bowl (it doesn't have to be perfect) and stir the cinnamon into the separated batter. Spread some of the plain batter into your prepared pan, and then dollop in some of the cinnamon batter. Repeat until all of the batter is in the pan.
Use a butter knife to swirl the batter in a figure-8 motion, being sure to go all the way to the bottom of the pan.
Optionally, you can sprinkle sugar on top of the batter before baking. Bake for 60-65 minutes, or until a cake tester comes out clean. Cool and enjoy!