Position a rack in the center of the oven and heat the oven to 350°F. Butter and flour a 10-cup decorative tube or bundt pan. Tap out any excess flour.
Melt the butter in a medium saucepan over medium-low heat. Once the butter is melted, cook it slowly, letting it bubble, until it smells nutty or like butterscotch and turns a deep golden hue, 5 to 10 minutes. If the butter splatters, reduce the heat to low. Remove the pan from the heat and pour the browned butter through a fine sieve into a medium bowl and discard the bits in the sieve. Let the butter cool until it’s very warm rather than boiling hot, 5 to 10 min.
Using a whisk, stir the sugar and eggs into the butter. (Since the butter is quite warm, you can use cold eggs for this.) Whisk until the mixture is smooth (the sugar may still be somewhat grainy), 30 to 60 seconds. Whisk in the mashed bananas, vanilla, and salt. Sift the flour and baking soda directly onto the batter. Pour the chocolate chips over the flour. Using a rubber spatula, stir just until the batter is uniformly combined. Don’t overmix.
Spoon the batter into the prepared pan, spreading it evenly with the rubber spatula. Bake until a skewer inserted in the center comes out with only moist crumbs clinging to it, 42 to 45 min. Set the pan on a rack to cool for 15 minutes. Invert the cake onto the rack and remove the pan. Let cool until just warm and then serve immediately or wrap well in plastic and store at room temperature for up to five days.
Photo: Scott Phillips