Heat oven: To 350°F (175°C). Coat a 9×13-inch baking pan with nonstick spray and line the bottom with parchment paper.
Make the batter: In a large bowl, beat egg whites until they hold firm peaks and set aside. In an empty mixing bowl, beat butter and 1½ cups of the granulated sugar until light and fluffy. Beat in egg yolks and vanilla. In a separate bowl, whisk flour, baking soda, baking powder, ½ teaspoon of the cinnamon, and salt together. Add banana to butter mixture and beat until combined. Add half the flour mixture, the sour cream, then the remaining flour mixture, beating each until combined. Fold in the egg whites.
Assemble the cake: Combine remaining ½ cup of the granulated sugar and 1 teaspoon cinnamon in a small bowl. Spread half of batter evenly in the prepared pan. Sprinkle with half of the cinnamon-sugar mixture and 1 cup of the chocolate chips. Dollop remaining cake batter over filling in spoonfuls. Use a rubber or offset spatula to gently spread it over the filling and smooth the top. Sprinkle batter with remaining cinnamon-sugar and remaining chocolate chips.
Bake the cake: For 35 to 40 minutes, until a tester inserted into the center of the cake comes out clean. Let cool in the pan.
To serve: Transfer cake to a cutting board and cut into squares.
