Heat cream, milk, cardamom pods, and cloves in a medium saucepan over medium-low heat, stirring occasionally, until steaming but not simmering, 3 to 5 minutes. Turn off heat, cover, and steep for at least 1 hour, then strain through a sieve (discarding spices) and return cream mixture to the saucepan over medium-low heat.

Prepare an ice bath by filling a large bowl ⅔ of the way with ice and water.

Whisk egg yolks and sugar together in a medium bowl for about 1 minute until mixture is silky and light yellow.

Whisk about ⅓ of the warm cream mixture into the egg mixture until combined. Add egg mixture to the remaining warm cream and stir to combine. Cook, stirring constantly, for 5 to 7 minutes, until custard thickens and coats a spatula.

Strain custard through a sieve into a medium bowl. Place bowl in the ice bath for about 5 minutes, stirring to cool down the custard.

Remove custard from ice bath and stir in rum, ground cardamom, ground cloves, and salt. Transfer to a lidded container, cover, and refrigerate at least 4 hours or overnight.

Taste chilled custard and adjust seasoning as needed. Pour into the chilled bowl of your ice cream maker and process according to the manufacturer’s directions. Transfer to a lidded container, cover, and freeze for at least 2 hours or overnight. Soften at room temperature for about 5 minutes before serving.