First, bring the filtered water to a boil and add the salt. Stir and let the pot simmer until the salt dissolves.
Allow the water to cool down for a half hour.
Meanwhile, add the basil leaves and the garlic cloves to the mason jar. When the salt water brine has cooled, pour it overtop.
Add the fermentation weight on top of the basil leaves and garlic, making sure that the veggies are completely submerged below the brine.
Secure the fermentation lid or loosely place a jar lid on top and let the jar sit on the counter for 7-10 days.
After 7-10 days, strain the liquid from the jar and save it for adding to other ferments, cooking, or making broth.
Take the basil and garlic and add it to a blender. Also add the nuts, olive oil, and parmesan cheese if using. Blend until smooth.
Use the pesto for pasta, pizza, or your favorite recipe. I have stored fermented pesto in the fridge for up to a week, but I haven't tested the shelf life for longer than that.