Preheat your oven to 350°F (175°C) and grease a 9x5-inch loaf pan. Mash 3 to 4 bananas until smooth, measuring about 1.5 cups.

In a large mixing bowl, combine the mashed bananas with ½ cup granulated sugar and ½ cup brown sugar. Add 2 beaten eggs, ⅓ cup melted butter and 1 teaspoon vanilla extract. Stir until smooth.

In a separate bowl, sift together 1.5 cups flour, 1 teaspoon baking soda, and ½ teaspoon salt. Gently fold this dry mixture into the banana batter until just combined.

In a medium bowl, beat together 8 ounces softened cream cheese and ⅓ cup powdered sugar until creamy. Add 1 egg yolk, 1 teaspoon lemon juice and 1 tablespoon flour. Beat until fully combined.

Pour half of the banana batter into the prepared loaf pan. Spread the cream cheese filling over the banana batter layer, then pour the remaining batter on top.

Bake for about 60-70 minutes. A toothpick should come out mostly clean. The top should be golden brown.

Let the loaf cool in the pan for about 10 minutes. Run a knife around the edges, then transfer it to a wire rack to cool completely.