Heat the coconut milk in a medium saucepan over medium heat until steaming but not boiling. Remove from the heat, stir in the Thai tea mix, cover, and let steep for 6 minutes.
Pour through a fine mesh sieve into a bowl, pressing firmly on the tea leaves with a spoon to squeeze out as much liquid as possible. Discard the leaves and rinse out the saucepan.
In the clean saucepan, whisk together the sugar, cornstarch, and salt, then whisk in the strained tea coconut milk. Cook over medium heat, whisking constantly, for 4 to 5 minutes, until it simmers and thickens slightly.
Remove from the heat and whisk in 3/4 cup of the condensed coconut milk and the vanilla. Press plastic wrap onto the surface and refrigerate for at least 6 hours or overnight.
Pour the chilled base into an ice cream maker bowl that has been frozen for at least 24 hours. Churn for 20 to 25 minutes, until thick and creamy.
Spread one third of the ice cream into a 9x5-inch loaf pan and drizzle with some of the remaining condensed coconut milk. Repeat the layers two more times, then swirl gently with a skewer.
Cover tightly and freeze for 4 to 6 hours, until firm. Let sit at room temperature for 10 minutes before scooping.