Preheat the oven to 350°F. Spray a 9x5-inch loaf pan with a nonstick spray. Line the bottom of the pan with a rectangle of parchment paper and spray the top of the parchment. Set the pan aside.
In a large bowl, whisk together 2 cups flour, 1 1/2 teaspoons baking soda, and 1/2 teaspoon salt. Set the dry mixture aside.
In a small bowl, mash 2 of the very ripe bananas with a fork, leaving some texture.
In a separate large bowl, beat the remaining 2 bananas with 1 cup sugar using an electric mixer (or vigorous whisking) for about 3 minutes, until the mixture is lighter and somewhat fluffy.
Add 3/4 cup melted and cooled butter, 2 eggs, and 1 teaspoon vanilla to the banana-sugar mixture. Beat until well combined, scraping down the sides and bottom of the bowl as needed.
Add the dry ingredients to the wet ingredients and mix just until incorporated. Do not overmix.
Fold the mashed bananas into the batter with a rubber spatula until evenly distributed.
Scrape the batter into the prepared loaf pan and tap the pan gently on the counter a few times to release any large air pockets.
Bake about 1 hour and 15 minutes, or until a toothpick inserted into the center comes out clean. A crack on top of the loaf is normal.
Cool the bread in the pan for 10–15 minutes. Then carefully turn the pan on its side and remove the loaf onto a wire rack. Allow the bread to cool completely before slicing.