In a small saucepan, heat the milk over medium-low heat until it's steaming but not boiling.
Add the chai tea bags to the hot milk and let them steep for about 5 minutes. Remove the tea bags, squeezing out any excess liquid, and discard them.
In the same saucepan, add the cocoa powder, semi-sweet chocolate chips, sugar, ground cinnamon, ground cardamom, ground ginger, ground cloves, ground black pepper, and a pinch of salt.
Whisk the mixture continuously over medium heat until the chocolate and cocoa powder are fully dissolved, and the mixture is smooth and heated through. Be careful not to let it boil.
Once the hot chocolate is ready, remove it from the heat and set it aside.
For Affogato:
In serving glasses or mugs, add a scoop of vanilla ice cream.
Pour a shot of strong brewed coffee or espresso over the ice cream in each glass.
Carefully ladle the prepared chai-spiced hot chocolate over the ice cream and coffee.
If desired, top with a dollop of whipped cream, chocolate shavings, and garnish with a cinnamon stick for an extra touch of elegance.
Serve the Chai-Spiced Hot Chocolate Affogato immediately while it's hot and the ice cream is melting into the delicious mixture.