On high heat, bring the filtered water to a boil.
Add the salt to the pot and stir until dissolved.
Remove the pot from the heat and allow to cool to room temperature.
In a mason jar, add the peppers, garlic, and carrots (if using). Pour the salt water over the vegetables. There should be enough water to completely cover the vegetables. Discard any unused salt water.
Place the silicone lid and then the fermentation weight overtop of the vegetables to keep them completely submerged in the salt water.
Secure your lid to the top of the jar. If you are using a regular mason jar lid, you will want to place it loosely on top.
Let the jar sit at room temperature for about 2 weeks.
Once two weeks has passed, remove the lid, silicone lid, and fermentation weight.
Separate the vegetables from the brine making sure to set the brine aside for later use.
Blend the vegetables in a blender adding brine until you reach the desired texture.
Taste the sauce and blend in any additional ingredients if desired (see notes).
Bottle your homemade fermented hot sauce. It will last in the fridge for at least 6 months.