Step 1: In a medium saucepan, combine the heavy cream, whole milk, black tea, cinnamon sticks, cardamom, ginger, cloves, and peppercorns. Heat over medium until it just reaches a simmer, then remove from heat and let steep for 20 minutes.
Step 2: While the cream steeps, whisk the egg yolks and sugar together in a medium bowl until pale and thick.
Step 3: Strain the tea and spices out of the cream mixture and return the liquid to the saucepan. Reheat gently. Slowly pour about half a cup of the warm cream into the egg mixture while whisking constantly to temper the eggs.
Step 4: Pour the tempered egg mixture back into the saucepan with the remaining cream. Cook over low heat, stirring constantly with a wooden spoon, until the custard thickens enough to coat the back of the spoon (about 170°F or 77°C). Do not boil.
Step 5: Strain the custard through a fine-mesh sieve into a clean bowl. Stir in the vanilla extract. Cover with plastic wrap directly touching the surface and refrigerate for at least 6 hours, preferably overnight.
Step 6: Churn the chilled custard in an ice cream maker according to the manufacturer’s instructions. Once it reaches a soft-serve consistency, transfer to a container and freeze for 2-4 hours until firm.
Step 7: To assemble the parfaits, layer the chai ice cream and crushed cookies in chilled glasses. Top with a dollop of whipped cream and a sprinkle of extra cookie crumbs.