Preheat your oven to 350°F (175°C) and line a 9x5-inch loaf pan with parchment paper, leaving some overhang for easy removal. Allow your cream cheese and eggs to reach room temperature for optimal mixing.
In a large bowl, mash the ripe bananas until smooth. Stir in the melted butter, sugar, eggs, and vanilla extract until well combined.
In a separate bowl, whisk together the flour, baking soda, salt, cinnamon, and nutmeg. Gently fold the dry ingredients into the wet mixture until just combined. Be careful not to overmix.
In a medium bowl, beat the softened cream cheese with an electric mixer until smooth and fluffy, about 2 minutes. Add the sugar, egg, flour, and vanilla extract, beating until completely smooth and free of lumps.
Pour half of the banana bread batter into the prepared loaf pan, spreading it evenly. Carefully spoon the cream cheese filling over the batter, leaving a 1/2-inch border around the edges.
Add the remaining banana bread batter on top, covering the cream cheese layer completely.
Using a butter knife or skewer, gently swirl the batters together by inserting the knife vertically into the batter and creating a figure-eight or "S" pattern throughout the loaf. Don't over-swirl, 5-6 swirls is typically sufficient.
Bake in the preheated oven for 60-65 minutes, or until a toothpick inserted into the center of the bread comes out clean or with a few moist crumbs. If the top begins to brown too quickly, cover loosely with aluminum foil after about 40 minutes of baking.
Allow the bread to cool in the pan for 15 minutes, then use the parchment paper overhang to lift it out onto a wire rack to cool completely. For the best texture and flavor, wait at least 30 minutes before slicing.