Place the carrots, onion, and garlic into a Dutch oven. Add the
water and a large pinch of salt to the pot. Cover and bring to a boil.
Lower to a simmer and cook until all the vegetables are very soft (a
knife should go through the thickest carrot easily), about 15
minutes.
Add the mustard, honey, and vinegar to the pot. Blend well
with an immersion (stick) blender to make a puree. Taste and
adjust the honey, vinegar, or salt for balance. Add the peppers, as
many as you can handle. Pulse the mixture with the immersion
blender again to break up the peppers into tiny flecks. Don’t
puree too much: the idea is to leave visible bits of pepper in the
sauce, not to make a homogeneous puree*.
Seal in sanitized bottles or keep refrigerated. The sauce keeps
for a year in bottles stored in a cool, dry location. If stored
unsealed in a refrigerator, use within a month.
* Artz says he’s tried this with fancier mustards but that
French’s works the best.* Be careful that you blend all the peppers, though. You don’t
want to leave big chunks of habanero in the sauce.