In a large pot, bring 10 cups water and 1 tablespoon salt to a boil. Add the cauliflower and potatoes and cook for 5 minutes. Remove from the pot and place in a colander set over a bowl to drain. Add the carrots and cook for 3 minutes. Remove the carrots from the pot and add to the colander. Add the jalapenos and cook for 2 minutes. Remove from the heat and add to the colander. Drain the cooked vegetables of excess water and place them in a 9-by-13-inch glass baking dish.
In a large heavy saute pan, heat the olive oil over medium heat. Add the garlic and cook until fragrant, about 4 minutes. Add the onion and cook until softened but not browned, about 2 minutes. Turn the heat off. Sprinkle a drop or two of vinegar into the oil. If it splatters, allow the oil to cool until no splattering occurs. Then add the vinegar, peppercorns, bay leaves, oregano and remaining 2 teaspoons salt. Stir to combine. Return the pan to medium heat and cook for 3 minutes. Pour the pickling liquid over the reserved vegetables and toss to combine. Cool the vegetables to room temperature, cover with plastic wrap and refrigerate overnight.