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Preheat the oven to 350°F with a rack in the center. Lightly grease an 8" square pan, then line it with a parchment sling.
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In a large saucepan, mash the banana with the sugars until well combined. Bring the mixture to a boil over medium heat, then cook, stirring frequently with a flexible spatula, until shiny, syrupy, and caramelized. The mixture should be thick enough so that when it’s removed from the heat and the spatula is dragged across the bottom of the pan, the line fills in after about 1 second. This will take about 4 to 8 minutes of cooking, depending on the ripeness of the bananas.
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Remove the pot from the heat, let cool for about 5 minutes, then add the butter, yolk, and vanilla. Stir until the mixture is creamy and emulsified.
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Whisk in the salt and baking powder, then stir in the flour with a flexible spatula until only a few dry streaks remain. Let the batter cool for about 5 minutes, then work quickly to stir in the nuts and chocolate (the chocolate will melt slightly). Transfer the thick, soft batter to the prepared pan and spread into an even layer (if the batter feels too thick to spread, use damp hands or a lightly greased offset spatula). Sprinkle with flaky salt if desired.
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Bake for 20 to 22 minutes, until the bars are set in the center and a toothpick comes out with no raw batter.
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Let cool completely in the pan (at least 2 hours) before transferring to a cutting board to slice and serve.
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Store the banana bread bars in an airtight container at room temperature for up to 4 days. Freeze, well wrapped, for longer storage.
