Make the palmiers: Roll out the puff pastry to an even thickness of 1⁄4 inch. Combine the turbinado sugar and cinnamon and sprinkle 1⁄4 cup of the mixture evenly over the dough. Using a rolling pin, roll over the pastry lightly. Fold both sides of the dough into the center so they meet in the middle of the sheet. Sprinkle 1 tablespoon of the cinnamon sugar over the dough. Roll over the dough again to lightly press the sugar into the dough. Fold the left side over the right side, creating a long log of dough. Cover the dough with plastic wrap and refrigerate for 20 minutes.
Preheat the oven to 425°. Remove the dough from the refrigerator and slice it crosswise into 3⁄4-inch discs. Transfer the cookies to a parchment paper–lined baking sheet, laying them cut-side up and several inches apart. Sprinkle the cookies with the remaining cinnamon sugar. Using a rolling pin, roll the cookies as thin as possible. Let rest for 30 minutes, then bake for 18 to 20 minutes, or until the palmiers are golden brown. Remove them from the oven and let cool.
In a large bowl (or using an electric stand mixer), beat the cream with the granulated sugar until stiff peaks form. Beat in the vanilla seeds and refrigerate until ready to use.
In a skillet, melt the butter over medium heat. Add the brown sugar and cook until bubbling, about 3 minutes. Add the bananas and cook, stirring and turning them occasionally, for 3 minutes. Remove the skillet from the heat and add the rum. Carefully light the rum on fire and let the flames subside. Return the skillet to the heat and cook for 2 minutes longer.
Arrange the palmiers on a serving platter in a single layer. Spoon the bananas flambé over the palmiers, filling in the gaps between the cookies. Dot the whipped cream over the palmiers, sprinkle with the hazelnuts and sea salt and serve immediately.
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