Preheat your oven to 350°F (177°C) and position the oven rack in the lower third. Grease a 9×5-inch loaf pan.
In a medium bowl, whisk together the flour, baking soda, cinnamon, and salt.
In a large mixing bowl, beat the butter and sugar until light and creamy, about 3 minutes.
Add the eggs one at a time, mixing well after each addition.
Mix in the mashed bananas, Greek yogurt, and vanilla extract until smooth.
Gradually add the dry ingredients and mix just until combined. Avoid overmixing to keep the Cinnamon Swirl Banana Bread soft and tender.
Stir together the cinnamon and sugar for the swirl.
Spread half of the batter into the prepared loaf pan.
Sprinkle the cinnamon sugar evenly over the batter.
Top with the remaining batter and gently spread it.
Use a butter knife to swirl through the center a few times without overmixing.
Bake for 55–65 minutes, covering loosely with foil halfway through if the top browns too quickly.
The bread is done when a toothpick inserted into the center comes out with only a few moist crumbs.
Cool in the pan for 1 hour before transferring to a wire rack.
Whisk together the icing ingredients and drizzle over the completely cooled loaf before slicing.