Mix whole milk, whipping cream, sugar, cinnamon sticks, tea, garam masala, peppercorns, cardamom pods, anise pods, and nutmeg together in a saucepan; bring to a simmer and cook for 20 minutes. Strain mixture through a colander into a large bowl. Add up to 1 cup more milk to cut spice level and sweetness to your liking.
Pour milk mixture into an ice cream maker and churn according to the manufacturer's instructions.
Stir chocolate into the churned milk mixture and freeze, stirring occasionally, until soft and creamy, 4 to 5 hours.
