For the banana bread: Position an oven rack in the bottom third of the oven and preheat to 325 degrees F. Generously spray a 9-by-5-inch loaf pan with nonstick spray and dust with flour.
For the cheesecake swirl: Combine the cream cheese, granulated sugar, sour cream and egg in a large bowl and beat with a hand mixer until well combined; set aside.
For the banana bread: Whisk together the flour, baking soda and salt in a medium bowl; set aside. Mash the granulated sugar and bananas in a large bowl to a paste. Whisk in the oil, vanilla and egg. Whisk in the flour mixture until just combined.
Reserve 3/4 cup of the bread batter. Spread the remaining batter in the bottom of the prepared loaf pan. Spoon the cream cheese mixture over the batter and put the reserved 3/4 cup batter in a line down the center of the pan. Insert the tip of a paring knife into the batter and drag it through and up to swirl 5 to 6 times.
Bake until the top is cracked and a cake tester inserted in the center comes out clean, about 1 hour. Cool on a wire rack for 30 minutes, then carefully invert onto a platter or cake stand and then flip upright. Cool completely, at least 1 1/2 hours. Dust with confectioners' sugar and serve.
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