Danish Creamery : Spiced Double Chocolate Tartlet

Ingredients

• 1 ⅓ cups all-purpose flour
• 3 Tablespoons Dutch-process cocoa powder
• ½ cup powdered sugar
• ¼ teaspoon Kosher salt
• 1 stick (8 Tablespoons) Unsalted Danish Creamery Butter, cold and cubed
• 1 large egg, cold
• 2 ¼ cups heavy cream, divided
• 2 cinnamon sticks, broken
• 2 star anise
• 10 green cardamom pods
• 4 egg yolks
• ¼ cup granulated sugar
• ⅛ teaspoon Kosher salt
• 1 teaspoon vanilla extract
• 7 ounces bittersweet chocolate, chopped
• 2 firm but ripe pears, such as Bartlett, Bosc or Anjou
• 1 lemon, halved
• ¾ cup sugar
• 1 Tablespoon corn syrup
• 3 Tablespoons water
• 1 teaspoon white wine vinegar