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Preheat the oven to 350°F. Spread the pecan pieces on a baking sheet and toast until just beginning to smell nutty and get a little darker, 10 to 15 minutes.
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In a large ovenproof skillet, melt the butter over medium heat. Add the brown sugar and maple syrup and cook over moderate heat, stirring, until the sugar is dissolved, about 2 minutes. Add the pears, cut side down. Spoon the sauce over the pears to coat, then bake for 30 minutes, basting with the pan sauce every 8 to 10 minutes.
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Return the skillet to the stovetop, minding the hot handle. Carefully transfer the pears to a plate. Place the skillet over low heat, then stir into the pan sauce the bourbon and salt; let simmer to thicken, about 2 minutes. Cool to further thicken, if desired.
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To serve, decoratively drizzle a little bourbon sauce onto 6 dessert plates. Add a dollop of whipped cream, top with a pear half, drizzle the pear with more bourbon sauce, sprinkle with toasted pecan pieces and a pinch of flaky or kosher salt, then serve immediately.