In a medium saucepan, combine heavy cream, sugar, and crushed cardamom pods. Heat over medium until sugar is dissolved and mixture begins to simmer, about 5 minutes. Remove from heat, sprinkle in bloomed gelatin, and stir until completely dissolved.

Strain the mixture through a fine mesh sieve into a measuring cup or bowl to catch the cardamom pods. Allow cooling slightly at room temperature for about 10 minutes.

Carefully pour the mixture into individual glasses, filling about three-quarters full. Cover with plastic wrap and refrigerate for at least 4 hours, or until set.

In a separate saucepan, combine white wine and sugar and bring to a gentle simmer. Peel and core the pears, then add them to the simmering mixture. Cook for about 15-20 minutes, turning occasionally, until tender.

Once panna cotta is set, remove from refrigerator. Top each glass with a poached pear and drizzle with poaching liquid. Garnish with mint or lemon zest.