Place tea leaves, if using, in a tea ball. Place tea ball or bag and vinegar in a small saucepan and bring to a boil over high heat. Lower heat and simmer, covered, 1 minute. Remove pan from heat and set aside, allowing tea to steep in the vinegar until cooled. Remove the tea ball or tea bag and gently squeeze the bag or leaves to extract as much vinegar as possible into the pot.
Transfer vinegar to a medium glass or stainless steel bowl. Add honey, thyme, shallots, and salt and pepper to taste; whisk until blended and smooth. Continuing to whisk, gradually add oil in a slow, steady stream until blended. The mixture will not emulsify. Transfer to a jar, cover tightly, and revrigerate for at least 4 hours. Store covered in refrigerator for up to 2 weeks. Shake well before serving. Makes about 1 1/3 cups.