Preheat your oven to 450 degrees.
Chop peeled carrots into 2" chunks and place on a rimmed baking sheet. Place the baking sheet in the oven and roast the carrots for 45 minutes, or until tender and beginning to char.
Approximately halfway through roasting the carrots, add the onion to the baking sheet and continue to roast the vegetables. Finally, add garlic cloves in the final five minutes of roasting.
Remove the roasted carrots, onion, and garlic from the oven and set the broiler to high. Place the Carolina Reapers on the baking sheet and set on the top rack, directly under the broiler, and broil peppers until beginning to char. *
Stir together apple cider vinegar, red wine vinegar, tomato paste, smoked paprika, and ground black pepper in a saucepan. When all vegetables are done roasting add them to the saucepan and gently simmer everything for 10 minutes (or longer) to ensure all of the vegetables have fully softened from cooking.
Transfer the hot sauce mixture to your blender and carefully puree everything together until the sauce is smooth and thin. Add water, if needed, to thin it into a pourable consistency then return the mixture to your saucepan and heat it to almost a simmer.
While the hot sauce is heated above 180 degrees, ladle the sauce into sterilized glass bottles, seal them shut with clean caps, and stand them upside down for five minutes to sanitize the caps.