In a medium saucepan, combine granulated sugar and water over medium heat. Stir continuously until the sugar is completely dissolved, which should take about 3-5 minutes. Remove from heat and allow the syrup to cool.

After the syrup has cooled, stir in the freshly ground cardamom and let the mixture sit for about 5 minutes to meld the flavors.

Wash, pit, and chop the ripe plums, then blend them with lemon juice and a pinch of salt until smooth and creamy.

Slowly pour the infused cardamom syrup into the blended plum mixture and blend again for about 30 seconds until integrated.

Strain the blended mixture through a fine-mesh sieve into a large bowl, discarding any solids left.

Cover the bowl of strained puree and refrigerate for at least 1 hour to chill thoroughly.

Pour the chilled mixture into your ice cream maker and churn according to the manufacturer's instructions, typically for about 20-25 minutes.

Transfer the churned sorbet into a freezer-safe container, cover tightly, and freeze for 2-3 hours before serving.