Preheat the oven to 350 degrees and grease a 9” cake pan with butter, or spray with cooking spray.
In the bowl of a stand mixer fitted with the paddle attachment (or in a large mixing bowl using a hand mixer), beat butter for about 30 seconds. Add sugar and granulated sugar and cream until light and fluffy. Scrape down the sides of the bowl.
Add egg yolks, bananas, flour, baking soda, and mix on medium speed until completely combined, scraping down the sides of the bowl as needed.
In a clean bowl, whip egg whites to stiff peaks. Using a rubber spatula, gently fold the beaten egg whites into the batter, taking care not to deflate the air bubbles.
Pour the batter into the prepared cake pan. Dollop tahini across the top of the cake and swirl using a knife or a toothpick.
Bake for 35-40 minutes, until a toothpick comes out clean when inserted into the center and the sides of the cake begin to pull away from the pan. Let cool slightly and serve warm with coffee or a cold glass of milk.