Gently crush the cardamom pods and place the shells and the seeds in a saucepan. Add the honey, cinnamon, salt, and milk. Warm over medium heat, stirring or whisking just until the honey dissolves and the mixture is steaming. (DO NOT boil.) Remove from the heat, cover, and steep for 30 minutes.
Place a fine mesh strainer over a large bowl and pour the mixture through it to remove all the seeds and shells. Add the cream and vanilla extract to the warm ice cream base. Stir to combine and chill in the refrigerator.
When ready to churn, whisk mixture again and pour it into the ice cream maker. Churn according to the manufacturer's instructions. Transfer the finished ice cream to an airtight container and place in the freezer until ready to serve.