This post is a summary of a recipe originally from thekitchn.com. I adjusted the recipe slightly to remove the ginger chunks from the tea.

Ginger Kombucha

Makes 1 gallon

Ingredients

3 1/2 quarts water
1 cup white sugar
4 bags black tea (or 1 tablespoons loose tea)
4 bags green tea (or 1 tablespoon loose tea)
2 cups pre-made unflavored kombucha (from your last homemade batch or store-bought)
1 scoby per fermentation jar
2- to 3-inch piece fresh ginger (See recipe note)

Bring the water to a boil. Remove from heat and stir in the sugar to dissolve. Steep tea until the water has cooled.
Once the tea is cool, remove the tea bags. Stir in the pre-made kombucha.
Pour the mixture into a 1-gallon glass jar and gently slide the scoby on top with clean hands. Cover the mouth of the jar with a few layers of cheesecloth or paper towels secured with a rubber band.
Keep the fermenting kombucha at room temperature, out of direct sunlight, and where it won’t get jostled. Ferment for 7 to 10 days, or until taste is desired.
Remove the scoby. Measure out your starter tea from this batch of kombucha to be added to the next batch.
Add grated ginger to kombucha. Infuse until tea has desired ginger flavor.
Strain the ginger from the kombucha. Stir kombucha to distribute scoby fragments. Add the kombucha to bottles. Leave about an inch of head room in each bottle. Store the bottled kombucha at room-temperature out of direct sunlight and allow 1 to 3 days for the kombucha to carbonate.
Refrigerate once carbonated.

Fermented the scoby on 7/10 with 3.5 Qrts water steeped in 8 bags of tea and 1 C sugar.
7/22 - Bottled kombucha with $\sim 1$ t finely grated ginger per 12 oz. Withheld 1 pint of kombucha for next batch. Adding 1 Qrt water steeped with 2 bags of irish breakfast tea and 1/4 C sugar to the scoby for storage. Batch produced 4 12 oz bottles, and 1 L plastic bottle.