Preheat oven to 350°F (177°C). Adjust oven rack to the lower third position. Grease a 9×5-inch loaf pan.
In a medium bowl, whisk together flour, baking soda, cinnamon, and salt. Set aside.
Using a mixer, beat butter and sugar on high speed until creamy and smooth, about 3 minutes.
Add eggs one at a time, mixing well after each addition.
Mix in mashed bananas, Greek yogurt, and vanilla extract until combined.
On low speed, slowly add dry ingredients into wet ingredients. Mix just until no flour pockets remain. Do not overmix.
In a small bowl, mix cinnamon and sugar for the swirl.
Pour half of the batter into the prepared pan. Sprinkle with the cinnamon-sugar mixture.
Add remaining batter on top and gently spread. Use a knife to lightly swirl down the center. Avoid over-swirling.
Bake for 55–65 minutes. Cover loosely with foil halfway through to prevent over-browning.
The Cinnamon Swirl Banana Bread is done when a toothpick inserted in the center comes out clean with a few moist crumbs.
Cool in pan for 1 hour, then transfer to a wire rack to cool completely.
Whisk icing ingredients together and drizzle over cooled bread before slicing.