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Preheat the oven to 350°F with a rack in the center. Grease a standard muffin pan generously with butter (do not skimp!). Place the muffin pan on a parchment-lined baking sheet.
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To make the topping: In a small saucepan, combine the butter, maple syrup, brown sugar, and salt over medium heat. Cook, stirring, until butter is melted. Continue cooking until the mixture comes to a full boil (i.e., big bubbles) around the edges of the pan, then set a 30-second timer. By the time it goes off, the mixture may not have boiled in the center of the pot – that’s OK (it’s better to under- than overcook this mixture). Remove the pan from the heat and stir in the pecans and vanilla.
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Distribute the pecan mixture evenly among the 12 muffin wells, being sure to get a mix of nuts and syrup in each one (you’ll need 1 heaping tablespoon per well; a tablespoon cookie scoop works well here).
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To make the muffin batter: In a large bowl, use a fork to stir together the banana and brown sugar until well-combined, with no lumps of sugar remaining. Add the sour cream or yogurt, oil, egg, and vanilla; whisk until well-combined. Whisk in the baking powder, baking soda, and salt. Add the flour and stir with a flexible spatula until no dry patches remain. Distribute the batter evenly among the wells of the muffin pan (about 1/4 cup per well; a scone and muffin scoop works well here).
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Bake the banana muffins, still on the baking sheet, for 22 to 25 minutes, until there are no moist spots on the muffins’ surface. Some caramel might bubble up (don’t worry: It cleans off the pan easily!).
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Remove the banana muffins from the oven and allow them to cool in their pan on a wire rack for 5 minutes. Then, nestle the wire rack onto a baking sheet and flip that over top of the muffins; invert the whole set-up so that the muffins release onto the wire rack with the baking sheet underneath. Sprinkle the hot muffins with flaky salt, then let cool slightly before serving.
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Storage information: Store the banana muffins in an airtight container at room temperature for up to 3 days.