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Preheat oven to 350 degrees F.
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Prepare a 9 inch by 5 inch loaf pan by oiling it and dusting it with flour. Alternatively, spray with a flour and oil baking spray.
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Mix the egg, brown sugar, granulated sugar, coconut oil, Greek yogurt (or sour cream) and vanilla extract (or paste) together.
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Mash bananas and stir into the sugar and oil mixture.
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Whisk all-purpose flour, baking powder, baking soda and salt together. Add the flour mixture to the banana/sugar mixture. Stir to combine ingredients but do not overmix.
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Prepare cream cheese filling. Combine egg, cream cheese, sugar and flour in a bowl. Mix with a hand mixer until the mixture is smooth.
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Pour about 1/2 of the banana batter into your prepared loaf pan. Smooth the top of the batter. Spoon all of the cream cheese filling over the banana batter. Smooth the cream cheese mixture and, using a spatula, spread the mixture evenly across the top of the batter and to the edges of the pan. Top with the remaining batter. Using a spatula, smooth the top to spread the batter to the edges of the pan.
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Bake for 50 minutes at 350 degrees F. or until the top of your banana bread is rounded and golden brown. (At 30 minutes, remove the bread from the oven and cover it with a layer of foil to keep the top of the bread from burning.) Return the covered bread to the oven. At the end of baking, you will want to check that the cake batter is set with a skewer inserted into the center of the cake. The skewer should come out clean. Remember that you have a cream cheese layer in the middle of your banana bread and that part of the bread will not give you a totally clean skewer. Remember, too, that this bread, with the cream cheese and the mashed bananas, is a very moist bread.
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Cool the bread on your counter. When it is cooled, cover it with plastic wrap and let it sit overnight before cutting.