Preheat your oven to 350°F (175°C). Grease and flour your 9x13 inch baking pan to prevent sticking.
In a large mixing bowl, whisk together the melted butter and granulated sugar until well combined. Add the eggs, sour cream (or yogurt), and mashed banana. Mix until smooth and creamy.
In a separate bowl, whisk together the flour, baking powder, baking soda, and vanilla extract. Gradually add the dry mixture to the wet ingredients, folding gently until just combined. Be careful not to overmix; a few lumps are okay.
In another bowl, combine the flour, room temperature butter, granulated sugar, brown sugar, cinnamon, and nutmeg. Use your fingers or a fork to mix until crumbly. The mixture should resemble coarse crumbs.
Pour the batter into the prepared baking pan and spread it evenly. Sprinkle the streusel topping generously over the batter, ensuring it's evenly distributed.
Place the pan in the preheated oven and bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean. The edges should be lightly golden.
Once baked, remove the cake from the oven and let it cool in the pan for about 10 minutes. Transfer to a wire rack to cool completely. Slice and serve warm or at room temperature.