Preheat your oven to 350°F (175°C). Grease your loaf pan with a little butter or line it with parchment paper for easy removal.
In a large mixing bowl, whisk together the melted unsalted butter, granulated sugar, and light brown sugar until well combined. Add in the eggs, one at a time, mixing well after each addition. Stir in the vanilla extract and pineapple Greek yogurt until smooth.
Next, fold in the mashed ripe bananas, grated carrots, crushed pineapple (with some juice), and raisins. If you’re using walnuts, now is the time to add them as well.
In another bowl, combine the all-purpose flour, baking soda, cinnamon, and salt (if using). Gradually add the dry mixture to the wet mixture, stirring until just combined. If you’re using the instant vanilla pudding mix, fold it in gently to incorporate.
Pour the batter into the prepared loaf pan, smoothing the top with a spatula. Bake in the preheated oven for 60-70 minutes, or until a toothpick inserted into the center comes out clean.
Once baked, remove the bread from the oven and allow it to cool in the pan for about 10 minutes. Then, transfer it to a cooling rack to cool completely.
While the bread is cooling, prepare the frosting. In a small saucepan, melt 1/2 cup of unsalted butter over medium heat, stirring frequently until it turns a golden brown color and develops a nutty aroma. Remove from heat and let it cool slightly.
In a mixing bowl, beat together 8 ounces of cream cheese (softened), the browned butter, and 2 cups of powdered sugar until smooth and creamy. If needed, add a splash of milk to achieve your desired consistency.
Once the bread is completely cool, generously spread the browned butter cream cheese frosting on top. Slice, serve, and enjoy every delicious bite!
