Preheat oven to 350°F. Spray an 8-inch round deep cake pan with baking spray with flour.: You will notice a warm, clean scent as the oven nears temperature, and preheating ensures even rise and baking. Preparing the pan prevents sticking, and the flour in the spray creates a fine barrier that helps the cake release smoothly. A common mistake is to skip preheating, which can cause uneven rising and a denser center. Check the oven thermometer if your oven runs hot or cold, because inaccurate temperature will alter baking time and the crumb's final texture.
For browned butter: In a medium saucepan, melt butter over medium heat. Cook until butter turns a medium-brown color and has a nutty aroma, about 10 minutes. Remove from heat, and let cool to room temperature.: In a medium saucepan, melt butter over medium heat. Cook until butter turns a medium-brown color and has a nutty aroma, about 10 minutes. Remove from heat, and let cool to room temperature. : At first the butter will foam and hiss gently, then the milk solids will begin to brown and release a toasty, hazelnut like scent that signals readiness. The color should be a warm amber, never black, and the sound will quiet when the water has evaporated. Cooling is important so you do not scramble the eggs in the batter or melt softened components. The common pitfall is leaving it on too long; burnt butter tastes bitter, so transfer off heat the instant it reaches a medium-brown hue and aromatic note.
For streusel: In a medium bowl, whisk together flour, brown sugar, cinnamon, and salt. Stir in butter until mixture is crumbly. Crumble with your fingertips until desired consistency is reached. Stir in pecans.: In a medium bowl, whisk together flour, brown sugar, cinnamon, and salt. Stir in butter until mixture is crumbly. Crumble with your fingertips until desired consistency is reached. Stir in pecans. : As you rub the butter into the dry ingredients, you will feel the mixture shift from powdery to pebble like clumps. The brown sugar will bind slightly, giving a tender crumble that bakes into crisp bits. Adding chopped pecans provides contrast and toasty flavor. Avoid overworking the mixture, because too fine a streusel will lose that pleasant bite; stop when you have a mix of pea to dime sized crumbs.
For cake: In the bowl of a stand mixer fitted with the paddle attachment, beat eggs, banana, pineapple, and vanilla at medium speed until combined, 1 to 2 minutes. Stir in browned butter.: In the bowl of a stand mixer fitted with the paddle attachment, beat eggs, banana, pineapple, and vanilla at medium speed until combined, 1 to 2 minutes. Stir in browned butter. : The batter will smell bright from the pineapple and vanilla , and you'll see the mashed banana swirl into a glossy mixture. Adding the cooled browned butter at this point disperses the toasty flavors evenly without cooking the eggs. A typical error is adding hot butter too soon, which can curdle the mixture; ensure the butter is at room temperature before folding it in.
In a medium bowl, whisk together flour, 3/4 cup (150 grams) granulated sugar, brown sugar, salt, baking powder, and 1/2 teaspoon (1 gram) cinnamon. Gradually add flour mixture to browned butter mixture, beating just until combined.: You will notice the dry mixture dust the batter before fully incorporating, then the texture will thicken into a cohesive, pourable batter. Whisking the dry ingredients first ensures the baking powder and spices are evenly distributed, which helps the cake rise uniformly and develop consistent flavor. Overmixing at this stage will activate gluten and produce toughness, so stop once you no longer see dry streaks.
In a small bowl, stir together remaining 1 tablespoon (12 grams) granulated sugar and remaining 1/2 teaspoon (1 gram) cinnamon. Spread half of batter into prepared pan. Sprinkle with one-third of streusel and cinnamon-sugar mixture. Top with remaining batter, smoothing top with an offset spatula. Sprinkle with remaining streusel.: The visual cues here are important, you want an even first layer that is not too thin, and a generous but not overwhelming streusel scatter. The cinnamon sugar will caramelize during baking, producing little pockets of crunch and sweetness. Use an offset spatula to smooth the top so it bakes evenly. Avoid packing the streusel into the batter, because pressed crumbs will sink and not crisp properly.
Bake until a wooden pick inserted in center comes out clean, 45 to 50 minutes, loosely covering with foil to prevent excess browning, if necessary. Let cool in pan for 15 minutes. Run a sharp knife around edges of cake to loosen sides. Invert onto a plate, and then invert again onto a wire rack.: During baking you will see the edges pull slightly from the pan and the top achieve a golden color, and when you tap the center it should sound set rather than jiggly. Tent with foil if the top gets too dark before the center is cooked. Cooling in the pan allows the crumb to finish setting, while the double invert helps the cake release without breaking the crust. Cutting too soon can cause the cake to crumble, so be patient and use a gentle hand when loosening the sides.
For glaze: In a small bowl, whisk together confectioners’ sugar, sour cream, and milk. Pour over warm cake.: In a small bowl, whisk together confectioners’ sugar, sour cream, and milk. Pour over warm cake. : The glaze should be smooth and glossy, with a slight tang from the sour cream that balances the sweetness. Pouring it while the cake is warm helps it spread and mingle with the streusel without melting away completely. If the glaze is too thick, add a little more milk , a teaspoon at a time, until pourable. A common mistake is making the glaze too thin, which causes it to run off; aim for a ribbon like stream when you lift the whisk.