Set your oven to 350°F and let it fully heat up. Line the loaf pan with parchment so the sides hang over. Grease the paper lightly, and the loaf will slide right out later.
Peel the bananas and drop them into a large bowl. Mash them with a fork until mostly smooth, leaving a few small lumps. Those little bits make every bite taste more like real banana.
Pour the melted butter over the mashed bananas and stir well. Add the sugar, beaten egg, and vanilla. Whisk until the mixture looks glossy and combined.
Sprinkle the baking soda and salt over the bowl. Add the flour and fold with a spatula. Stop as soon as no dry streaks remain, because overmixing makes the bread tough.
Beat the soft cream cheese in a separate bowl until smooth. Add the egg, sugar, and flour. Whisk until silky, with no lumps left, so it swirls neatly.
Spoon about half of the banana batter into the pan. Dollop half of the cream cheese mixture on top. Repeat with the remaining batter and filling for pretty layers.
Insert a butter knife into the pan and drag it through the layers. Make a few gentle figure-eight motions. Don't overdo it, or the cream cheese will blend in and vanish.
Slide the pan into the oven and bake for about 60 minutes. The top should look golden and the center should feel set. Test with a toothpick in the banana batter, not the cream cheese.
Let the loaf rest in the pan for about 15 minutes. Lift it out with the parchment and move it to a wire rack. Cool it completely, since the swirl firms up as it chills.