Pear and Frangipane Tart - The Local Palate

Ingredients

• 1 (7-to-10-ounce) sheet puff pastry, defrosted if frozen but still cold
• 4 firm pears, identical in size and shape 2¼ cups sugar, divided
• 1 whole star anise pod
• ½ teaspoon pink peppercorns
• 4 tablespoons unsalted butter, at room temperature
• 3 tablespoons almond paste, at room temperature
• 1 egg, lightly beaten
• 3 tablespoons flour, sifted