Peel the pear, cut into 8 segments, and remove seeds. Heat a grill pan, sauté pan, or your grill to medium-high heat. Place the pear segments in the pan or on the grill and cook until golden brown and sporting defined grill marks. Cover and infuse the smoke for 10 minutes.

Remove the grilled pears and set aside.

In a small pan over low heat, toast cinnamon, peppercorns, star anise, and cardamom pods, stirring often, until fragrant (3–4 minutes). Add 1 ½ cups water and sugar and bring to a boil. Stir until sugar dissolves. Add pear segments to the pan and return syrup to a boil. Remove the pan from the stove, cover, and set aside for an hour to poach pears. Remove pears from syrup and set aside. Place syrup over medium-high heat; simmer to reduce by it half. Strain syrup and cool completely before using.