Combine the vinegar, water, sugar, and salt in a small saucepan. Place over medium heat and warm until the sugar and salt dissolve.
Trim the ends and cut the carrots in equal lengths. Trim away the sides of the carrots so that you end up with a neat orange rectangle. Carefully cut the carrots into slim planks. Stack two or three of the planks and cut them into matchsticks. Repeat until all your carrots are reduced to matchsticks.
Set the carrots aside and prep one red pepper by slicing off the ends. Cut the pepper into two equal halves and trim away the interior pith and seeds. Thinly slice the red pepper so that they roughly match the size and shape of the carrots.
Take a small lime and trim off both ends. Using a sharp paring knife, carefully slice away three or four strips of zest. Switch back to a chef knife and mince those strips into confetti.
Take a clean, wide mouth pint jar and place 1/2 teaspoon each black peppercorn and crushed red chili flakes in the bottom. Add two garlic cloves and the lime zest confetti. Add the cilantro leaves and stems.
Pack the carrot and red pepper matchsticks into the jar.
Once all the carrots and peppers are in the jar, pour the warm brine over the vegetables.
Place a lid on the jar and refrigerate it for at least 24 hours before eating.