1. Using a blender, immersion blender, or whisk, mix all ingredients except tea until well-combined. (If using an immersion blender or whisk, combine milk and egg yolks, then add cane sugar and sea salt, then heavy cream.)
2. Pour ice cream base into a pot over medium-low heat. Cook, stirring frequently, until the mixture reaches 155 degrees. Remove from heat and add tea bags. Cover and steep for 10 to 15 minutes. After steeping, remove teabags and squeeze excess liquid from bags back into pot. Strain mixture, then transfer to a heat-safe container and cover. Refrigerate for at least 4 hours or overnight.
3. After mixture has chilled, whisk well, then pour into ice cream machine. Follow manufacturer’s instructions to churn ice cream. Transfer to a freezer-safe bowl, cover, and freeze overnight.