Select a medium saucepan that will accommodate the pears snugly in an upright position, allowing space for the stems to fit with the lid in place.
Core the pears from the bottom to remove the seeds, leaving as much of the flesh as possible. Peel the pears, leaving the stems attached. Trim the bottoms slightly, so the pears can stand up straight. Put them in the saucepan and add the juice. It’s normal for the pears to turn on their sides and float at first. If you have a large strainer, set it over the pears gently to keep them submerged.
Break open the cardamom pods and remove the seeds. Crush the seeds to a gritty powder in a mortar with a pestle or on a cutting board with the back of a wooden spoon.
Add the cardamom seeds and bay leaf to the saucepan. Bring to a boil over high heat. Decrease the heat to medium and simmer until the pears are tender, 20 to 45 minutes. To test the pears for tenderness, insert a paring knife into the thickest part of the pears and lift; the pear should slip off easily.
Using tongs, grasp the pears by the stems and lift them out of the saucepan, allowing several seconds for the juice to drain well. Set them on a plate.
Increase the heat to high and bring the juice to a boil. Boil until the juice is reduced to about 3⁄4 cup, about 5–7 minutes. It should be a fairly dense syrup, thick enough to coat a spoon. If any juice has accumulated around the pears, carefully tip the plate and let it run back into the saucepan. Remove saucepan from the heat and let the syrup cool for about 10 minutes. Discard the bay leaf.
Using a large spoon, drizzle the syrup over the pears. Lift the pears with the tongs and transfer them to dessert plates. Drizzle again with the syrup and serve at once.