Whisk vinegar, water, and sea salt together in a small saucepan. Bring to a low boil over medium-high heat, reduce heat, and simmer until salt is completely dissolved, about 3 minutes. Set aside.
Peel carrots and cut them into 1/2-inch diagonal slices. Cut onion into quarters. Cut each quarter into 3 strips. Cut stems off jalapenos and cut each jalapeno into 6 strips. Slightly crush each garlic clove.
Warm oil in a nonstick skillet over medium heat, add carrots, and cook, stirring occasionally, for 6 minutes. Add bay leaves, peppercorns, oregano, and cumin seeds. Cook and stir for 2 minutes. Add onion, jalapenos, and garlic. Cook, stirring occasionally, until vegetables are tender and fragrant but not soft, about 15 minutes.
Place vegetables in a 24-ounce wide-mouth canning jar. Pour in the cooled vinegar mixture until liquid reaches 1 inch from the top. Pour olive oil on top and secure the lid. Allow to cool to room temperature. The carrots are ready to serve after 1 hour but best after sitting for 24 hours.