Prep your tea leaves at least 1 days in advance. Pour loose leaves into a medium bowl. Pour boiling water over the leaves and allow to steep for 10 minutes. Strain and rinse with cool water. Pick through the unfurled leaves and discard any obvious twigs or woody stems.
Return to bowl and cover with cold water. Let sit for at least 1 hour. Drain again and rinse.
Squeeze out the tea leaves to get rid of excess water. Place leaves into your food processor or blender.
Add garlic, ginger, shallot, sesame oil, vegetable oil, lemon juice, vinegar, fish sauce, and salt.
Process until mixture is similar to the texture of pesto. You may need to scrape down the sides of your processor a few times.
Pour mixture into a storage container and place in the refrigerator for at least 24 hours- dressing is best after 2-3 days of refrigeration.