Sauté (optional but flavorful). Heat the oil in a large pot over medium heat (if using). Add carrots and cook 2-3 minutes. Stir in onion, garlic, jalapeños, and cauliflower if using. Cook another 2 minutes, stirring a bit, until fragrant.
Pour in vinegar and water. Stir in salt, sugar, bay leaves, peppercorns, oregano, and thyme. Bring to a simmer, then reduce heat and cook 8-10 minutes, until carrots are crisp-tender and jalapeños turn a duller green.
Pack the vegetables into clean jars. Ladle hot brine over the top, making sure everything is submerged. Cool to room temp, seal, and refrigerate. For best flavor, let sit 24 hours before eating.
