First, roughly chop the peppers, carrots and garlic. Pack them into a large jar, leaving at least 1 inch of head space. The mixture may rise a bit when fermenting.
Next, mix 1 quart unchlorinated water with 3 tablespoons sea salt. Pour just enough brine over the mixture to cover it, pressing them down a bit as you go. It is important to keep the mixture covered with brine to avoid spoilage. Check this daily.
Screw on the lid and set the jar away from direct sunlight to ferment for at least 1 week. I fermented for 8 weeks. Ideal temperatures are between 55-75 degrees F. The most active fermentation period is between 1-2 weeks, so be sure to monitor it during this time. “Burp” the jars often by unscrewing the lid a bit to let out some of the accumulating gases. Or, use an airlock or membrane for easier fermenting. See our page, “How to Make Fermented Pepper Mash”, for further instruction.
After 1-2 weeks, the fermenting activity will diminish and the brine will turn cloudy and taste acidic.
When satisfied with your fermenting time, pour the contents, including brine, into a pot along with the remaining ingredients. Bring to a quick boil. Reduce heat and simmer for 15 minutes.
Cool, then process with a food processor until nice and smooth.
Pour into sterilized jars and seal. Refrigerate and enjoy. Tastes even better if you leave it mingle a week or longer.