In a medium saucepan, stir together the milk, heavy cream, 1 Tbsp of sugar and pinch of salt. Cook on medium heat until the mixture comes to a boil.
In a medium bowl, whisk together eggs and 1/4 cup sugar. Add approximately 1/2 cup of the hot milk mixture to the egg mixture, whisking as you add it slowly. Continue to add the milk mixture 1/4 cup at a time until it’s all been mixed in. Transfer the mixture back to the saucepan.
Cook over medium-low heat, stirring constantly, until the mixture thickens and coats the back of a metal spoon. Remove from heat and stir in vanilla extract, vanilla bean paste and ground cardamom. Add the custard to a large bowl and cover with plastic wrap, making sure the plastic wrap touches the surface of the custard to prevent a film from forming. Chill completely, approximately 2 hours in the refrigerator.
Add the custard mixture to your ice cream maker and churn according to the manufacturer’s instructions. In the last few moments add in the chocolate chips.
Pour into an airtight container. Chill for a minimum of 6 to 8 hours before serving.