For whole chiles, prick jalapeños all over with the tip of a sharp knife. For slices, stem jalapeño chiles and cut into quarters lengthwise.
In large saucepan, heat olive oil. Add onions and cook just until softened, about 3 minutes. Add carrots and chiles and cook for 5 minutes. Add vinegar, water, salt, cauliflower, oregano and bay leaves. Bring mixture to a boil and then simmer, uncovered, for 10 minutes. Taste for seasoning and add more salt if needed.
Spoon vegetables into clean glass jars and let cool completely. When cool, cover and store in the fridge at least 24 hours, to let mixture pickle completely.