In a large pot, combine the sassafras root bark, sarsaparilla root, wintergreen leaf, licorice root, cinnamon stick, and vanilla bean. Add 1 gallon of water and bring to a boil. Reduce heat and simmer for 20 minutes.
Remove the pot from the heat and stir in the granulated sugar and molasses until dissolved. Allow the mixture to cool to room temperature.
Once cooled, strain the liquid through a fine mesh sieve or cheesecloth into a clean container. Discard the solids.
Sprinkle the active dry yeast over the surface of the liquid and gently stir to combine. Transfer the liquid to glass bottles, leaving at least 1 inch of headspace at the top.
Seal the bottles with the swing-top lids and allow them to ferment at room temperature for 3-5 days, or until carbonated to your liking. Burp the bottles daily to release excess carbonation.
Once fermented, refrigerate the root beer to halt the fermentation process. Serve chilled and enjoy!