Scald the milk and cream. Use a small clip to anchor the tea bags to the side of the pot. Combine milk, heavy cream, and red food coloring (if using) in a small sauce pot over medium heat, stirring constantly. When you start to see bubbles around the edges of the milk, tilt the pot forward. When you see lots of bubbles on the bottom of the pot, turn the heat off and let the mixture continue steeping for an additional 10 minutes, stirring occasionally.If you tilt the pot forward and don't see lots of bubbles, keep stirring over medium heat and repeat until you do. Do NOT boil.
Ribbon eggs and sugar. In a heat-safe bowl, vigorously whisk together eggs and sugar until slightly pale and creamy.
Temper tea into egg mixture. Use a spatula to press as much liquid out of the tea bags as possible, then discard the tea bags. Place the bowl of eggs and sugar on top of a folded kitchen towel to hold it in place. With the whisk in your dominant hand, slowly drizzle the hot tea mixture into the egg mixture, whisking constantly so the eggs don't scramble.
Cook to thicken. Once all the milk has been added, whisk for about 20-30 seconds, then transfer the mixture back to the pot over low-medium heat. Stir constantly with a wooden spoon, scraping the bottom of the pot, until the mixture reaches "nappe" consistency, meaning it coats the back of the wooden spoon.Do NOT boil. Keep it at a gentle heat and be patient, it will thicken after a few minutes.
Strain out any lumps. Pour the mixture through a wire mesh strainer into a heat-safe container.
Chill. Immediately place the container in an ice bath (or cold water bath) to bring the temperature down enough that you can put a lid on it (stir it occasionally to speed up this process), then place it in the fridge for at least 6 hours, ideally overnight, before churning.
Churn. According to your ice cream maker's instructions. Transfer churned ice cream to an airtight container. Press a sheet of plastic against the surface of the ice cream, place the lid on the container, and freeze for at least 2 hours before serving.