Combine 2 quarts water, tea, sarsaparilla, birch, mint, star anise, ginger, and vanilla in a medium saucepan. Bring to a boil
Reduce to a simmer, and cook for 10 minutes.
Remove pot from heat, cover, and let sit for 2-2 1/2 hours.
Use a mesh filter and a cheese cloth to strain the contents into a large pot.
Add the remaining water along with the sugar and molasses. Stir until dissolved.
Let cool to 75°F, then stir in yeast and let sit for 15 minutes.
Pour the mixture into sanitized bottles, leaving about 2 inches of space on top. Screw on caps.
Keep the bottles at room temperature for 36 hours, then open a bottle to see if it is carbonated enough. If not, reseal the bottle and let rest for another 12 to 24 hours until desired carbonation is reached.
Keep bottles in refrigerator for two days before drinking. Root beer can be kept in the refrigerator for up to one month.