12 tablespoons (1 1/2 sticks) unsalted butter, cut into small pieces
1 1/4 cups granulated sugar
4 large eggs
3/4 cup plus 1 tablespoon all-purpose flour
Pinch of salt
8 ounces cream cheese, at room temperature
1 large egg yolk
Vegetable-oil cooking spray
1/4 cup plus 2 tablespoons confectioners' sugar
1/2 teaspoon pure vanilla extract
1/2 cup mashed very ripe banana (1 medium banana)
Heat oven to 350 degrees. Spray a 9-by-13-inch baking pan with vegetable-oil spray. Bring a saucepan of water to a boil; remove from heat. Place both chocolates in a heat-proof bowl; set over saucepan. Stir occasionally until completely melted.
Meanwhile, combine butter and granulated sugar in the bowl of an electric mixer fitted with the paddle attachment; beat on medium-low speed until light and fluffy, 3 to 4 minutes. Add 3 eggs; beat to combine. Scrape sides of bowl; add chocolate, 3/4 cup flour, and salt. Mix until just combined, 15 to 20 seconds, scraping sides of bowl once.
In a food processor, process cream cheese until smooth and creamy, 25 to 30 seconds. Scrape down sides of bowl using a rubber spatula; add egg yolk, confectioners' sugar, vanilla, remaining tablespoon flour, and remaining egg. Process until smooth, about 1 minute. Transfer to a bowl; fold in mashed banana using a rubber spatula.
Spread chocolate batter into prepared pan. Using a rubber spatula, make three trenches in batter, and fill with cream-cheese batter. To marble the top, run the tip of a knife back and forth across the two batters.
Bake until set, about 40 minutes. Let cool on a wire rack for 30 minutes before cutting.