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For the roasted bananas:
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Preheat oven to 400u00b0F and arrange bananas in a single layer in a baking dish; sprinkle with brown sugar and diced butter. Roast for 25 minutes, gently stirring mixture halfway through. Cool slightly.
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For the bars:
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Reduce oven temperature to 350u00b0F and coat a 13 x 9-inch baking dish with nonstick spray.
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In a medium bowl, whisk together flour, baking powder, baking soda, salt, cinnamon, allspice, and cardamom.
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In a small bowl, combine buttermilk, banana, and vanilla.
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In a large mixer bowl, beat butter and sugar on medium speed until pale and fluffy. Add eggs and beat well. Reduce speed to low and add 1/2 of the flour mixture to the sugar mixture; beat just until combined. Add buttermilk mixture, then finish with remaining flour mixture.
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Gently fold in roasted banana, then pour mixture into prepared baking dish and smooth top with an offset spatula. Bake 18 to 20 minutes, until golden and a toothpick inserted in the center comes out with a few crumbs attached. Remove from the oven to cool completely in the pan on a wire rack.
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For the glaze:
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Place butter in a small saucepan over medium heat. Cook, stirring constantly, until it foams, turns clear, and then turns a deep brown, about 6 minutes. Cool slightly.
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In a small bowl, sift powdered sugar; whisk in browned butter, maple syrup, and milk until smooth.
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Pour over cake and spread evenly with an offset spatula, then sprinkle with toasted pecans. Let glaze set before cutting into bars.
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Store leftovers in an airtight container at room temperature up to 2 days.