Give the jalapenos a good rinse and then cut them into 1/4 inch slices (or thinner if you want). Discard the stems. Peel the carrots and cut into similar sized slices.
Peel and quarter the onions, then chopping them into half-moon shaped slices. Peel and roughly chop the garlic cloves.
Heat a glug of oil in a large saucepan over medium heat. Saute the onions and garlic for a few minutes.
Add the spices to the onion mixture: 2 teaspoons cumin seeds, 2 teaspoons Mexican oregano, 1 teaspoon black peppercorns. I usually give the spices a quick crush in the molcajete before adding them. Feel free to use powdered spices if you don't have seeds or peppercorns on hand.
Add the jalapenos and carrots to the saucepan along with the remaining ingredients: 6 cups white vinegar, 4 cups water, and 4 tablespoons kosher or sea salt. Cover and bring to a boil. Once boiling remove the pan from the heat. I usually raise the heat to high to get it to a boil.
Fill 4 quart-sized jars with the mixture (or your choice of smaller glass jars). I use tongs to fill the jars with the jalapenos, and then use a measuring cup to fill the jars to the brim with the brine. You can give them a taste test now for a preview, but they won't have full flavor until they rest overnight in the brine.
Let the jars cool on the counter for a bit, then cap them and store them in the fridge where they will keep for weeks at a time.