Preheat the oven
Set the oven to 350°F (175°C) and grease a 4x8-inch loaf pan.
Prepare the banana bread batter
In a mixing bowl, mash the bananas until smooth. Stir in the melted butter, ensuring an even consistency. Incorporate the baking soda and salt, followed by the sugar, beaten egg, and vanilla extract. Gradually mix in the flour until fully combined.
Prepare the cream cheese filling
In a separate bowl, use a hand mixer or stand mixer to blend the softened cream cheese with the sugar, flour, and egg until smooth and creamy.
Layer and swirl the batters
Pour half of the banana bread batter into the prepared loaf pan. Distribute half of the cream cheese mixture in small dollops over the batter. Add the remaining banana bread batter, then top with the remaining cream cheese filling in dollops. Using a butter knife, gently swirl the cream cheese into the batter with vertical and horizontal strokes.
Bake
Transfer the loaf pan to the preheated oven and bake for 55 to 60 minutes, or until a toothpick inserted into the center emerges clean.
Cool and store
Allow the bread to cool slightly in the pan before transferring it to a wire rack to cool completely. Store covered at room temperature for up to four days.