Preheat your oven to 350°F (175°C) and prepare your 9x5-inch loaf pan by greasing it or lining it with parchment paper.

In a large mixing bowl, whisk together one large egg, ½ cup of light brown sugar, and ½ cup of granulated sugar until smooth. Then add ⅓ cup of coconut oil, ½ cup of sour cream, and 1 teaspoon of vanilla extract, mixing until creamy.

Mash 2 large ripe bananas in a separate bowl until smooth and stir them into the wet mixture, ensuring they're well integrated.

In another bowl, sift together 1 ½ cups of flour, 1 teaspoon of baking powder, ½ teaspoon of baking soda, and optional ¼ teaspoon salt. Gently fold the dry ingredients into the banana mixture without overmixing.

Pour about two-thirds of the batter into the prepared pan and smooth the top.

In a mixing bowl, whisk together 8 ounces of softened cream cheese, 1 egg, ¼ cup of sugar, and 2 tablespoons of flour until smooth. Spread this mixture over the batter in the pan.

Carefully spoon the remaining batter on top of the cream cheese filling and smooth it gently.

Bake in the preheated oven for 48-50 minutes, checking for doneness with a toothpick.

After baking, allow the bread to cool in the pan for 15 minutes before transferring it to a wire rack to cool completely.