Gently crush cardamom with a rolling pin or the bottom of a skillet to slightly crack open pods without releasing seeds. Combine cardamom, juice, vinegar, sugar, lemon juice, and salt in a medium saucepan over medium heat, stirring until sugar dissolves. Bring to a simmer. Add pears; add water if needed to completely submerge pears. Cover with lid slightly ajar and simmer, turning very gently occasionally, until pears are tender but not mushy, about 30 minutes.
Using a slotted spoon, transfer pears to a plate. Increase heat and boil poaching liquid until reduced to 1 cup, 10–15 minutes.
Notes
DO AHEAD: Can be made 8 hours ahead. Cover and refrigerate pears. Let syrup stand at room temperature. Rewarm syrup before Serving.Alternate poaching liquids: Poire Avec Orange 1 1/2 cups orange juice without pulp 1/2 cup packed brown sugar 1/4 cup white sugar 1 tablespoon vanilla extract 1 teaspoon ground cinnamonHoney-Ginger 2 cups white grape juice 1 cinnamon stick, broken in 1/2 2 tablespoons honey One 3/4-inch piece fresh ginger, peeled, and finely chopped 1 vanilla bean, split lengthwise