1. Combine peppers and salt in the bowl of a food processor, pulse until finely chopped. Transfer to a glass jar, cover, and let sit at room temperature overnight.
2. Add vinegar and stir to combine. Cover and let mixture sit at room temperature for 1 day. (You can ferment up to 7 days, if desired.) Transfer to blender, add carrot, and blend until smooth. Strain mixture through a sieve and into a clean glass bottle or jar. Seal tightly and store in refrigerator.