Pack the carrots tightly into a clean, sealable glass jar, leaving about ½ inch headspace at the top. Trim carrot sticks as needed to fit your jar.
Add the minced garlic, black peppercorns, and jalapeno slices to the jar, distributing them evenly around the carrots.
In a small saucepan, combine the vinegar, water, sugar, and salt. Bring the mixture to a boil.
Reduce the heat and simmer for about 2 minutes, stirring until the sugar and salt are completely dissolved.
Carefully pour the hot brine over the carrots until they are fulling submerged. Leave about ¼ inch headspace at the top of the jar.
Allow the jar to cool completely at room temperature, then seal with a lid and place in the refrigerator.
Refrigerate for at least 24 hours before eating. Flavor improves after 2 to 3 days.