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Lightly grease an 8 1/2" x 4 1/2" loaf pan and line it with a parchment sling.
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Tear or cut peeled bananas into large (2") pieces and place in an 8" square pan, a cast iron skillet, or a small rimmed baking sheet. Cover with the brown sugar and place in the oven.
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Preheat the oven to 325°F with the bananas inside. Roast the bananas for 20 to 25 minutes total, stirring every 5 to 10 minutes, until the bananas are very soft and the brown sugar is bubbling.
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Carefully transfer the hot mixture to a large bowl and mix vigorously with a potato masher; you should have a liquidy mixture with some small lumps of banana remaining. Set aside to cool for 5 minutes.
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Once slightly cool, add the oil, egg, and vanilla to the bowl with the bananas and whisk for 1 to 2 minutes, until the mixture is fully emulsified.
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Add the flour, baking powder, baking soda, and salt, and stir with a flexible spatula to thoroughly combine. Transfer the batter to the prepared pan, smooth the top, and sprinkle with turbinado or sparkling sugar.
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Bake the banana bread for 45 to 50 minutes, until a toothpick or paring knife inserted into the center of the loaf comes out clean; the internal temperature should register at least 205°F when measured with a digital thermometer.
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Remove the banana bread from the oven and let it cool in the pan on a wire rack for 15 minutes. Then remove the loaf from the pan, peel away the parchment, and let it cool completely before slicing and serving.
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Store leftover banana bread, well-wrapped at room temperature, for 4 days. Freeze for longer storage.
