Prepare the Pan: Preheat the oven to 350°F (175°C). Grease a 9-by-13-inch (23-by-33-cm) baking pan or line it with parchment paper. This ensures that the cake will not stick to the pan, making it easier to slice and serve once baked.

Make the Streusel: In a small bowl, combine the flour, brown sugar, cinnamon, and salt. Cut in the cold butter using a pastry cutter or your fingertips until coarse crumbs form. Refrigerate while preparing the batter to keep the streusel crisp.

Prepare the Cream Cheese Filling: Beat the softened cream cheese and sugar until smooth. Mix in the egg and vanilla until fully combined. Set aside. This filling will add a creamy texture and tangy flavor that complements the banana cake.

Mix the Dry Ingredients: In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. This step ensures that the leavening agents are evenly distributed throughout the batter for consistent rising.

Cream the Butter and Sugar: In a large bowl, beat the softened butter and granulated sugar for 2 to 3 minutes until light and fluffy. This process incorporates air into the mixture, which helps the cake rise and creates a tender texture.

Add the Wet Ingredients: Beat in the eggs one at a time, followed by the vanilla. Mix in the mashed bananas until combined. Fold in the sour cream. The bananas add moisture and flavor, while the sour cream contributes to a tender crumb.

Finish the Batter: Add the dry ingredients in two additions, mixing only until no dry streaks remain. The batter should be thick and smooth. Overmixing can lead to a dense cake, so mix just until combined.

Assemble the Cake: Spread about two-thirds of the batter evenly into the prepared pan. Spoon the cream cheese filling over the batter and gently spread it into an even layer, leaving about a 1/2-inch border around the edges. Carefully dollop and spread the remaining batter over the filling. This layering technique helps keep the cream cheese filling centered.

Add the Streusel: Sprinkle the chilled streusel evenly across the top of the batter. This will create a crunchy topping that contrasts nicely with the soft cake and creamy filling.

Bake: Bake for 45 to 50 minutes, or until the topping is golden brown and a toothpick inserted into the cake portion comes out clean or with a few moist crumbs. Avoid inserting the toothpick directly into the cream cheese layer when checking doneness to ensure accurate results.

Cool: Place the pan on a wire rack and cool for 20 minutes before slicing. The cream cheese filling will continue to set during this time, making it easier to cut clean slices.

Serve: Slice into 12 portions and serve slightly warm or at room temperature. This cake is versatile and can be enjoyed at any time of day.