Easy recipe Vanilla-Spiced Caramel and Pear Tart

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one sheet frozen puff pastry (half of seventeen.about three-ounce package), thawed, or one fourteen- to sixteen-ounce package all-butter puff pastry (one to two sheets, depending on brand), thawedabout three tablespoons unsalted butterone/two cup sugarone cinnamon stickone whole star aniseabout three whole clovesGenerous pinch of coarse kosher saltone/two vanilla bean, split lengthwiseabout six medium firm but ripe Anjou pears, peeled, halved lengthwise, coredone quarter cup (one/two stick) unsalted butterone/two vanilla bean, split lengthwise in halftwo cinnamon sticks, broken in halftwo whole star aniseabout six whole clovesone quarter cup sugarone large eggGenerous pinch of coarse kosher saltone one/two tablespoons all purpose flourone egg white, beaten to blendSpecial equipment: ten-inch-diameter springform panIngredient Info: All-butter puff pastry is available frozen at Whole Foods markets. One fourteen- to sixteen-ounce package contains two eleven-inch rounds. Whole star anise is available in the spice (Recipes by ingridients spice) section of some supermarkets.. .