Preheat oven to 400°.
Place peppercorns, thyme, marjoram, oregano, and bay leaves on a triple layer of cheesecloth. Gather the edges of the cheesecloth together, and tie securely. Remove white papery skin from garlic head (do not peel or separate the cloves); trim about 1/4 inch from top of garlic. Combine the garlic, carrot, oil, and onions in a Dutch oven. Bake, uncovered, at 400° for 30 minutes. Stir vegetables; add spice bag to onion mixture. Bake an additional 25 minutes or until vegetables are tender. Peel garlic cloves; place garlic, vegetables, and spice bag in a large bowl.
Drain jalapeños over a bowl, reserving liquid. Place the Dutch oven over medium-high heat; stir in the reserved jalapeño juice and vinegar, scraping pan to loosen browned bits. Add water, and bring to a boil. Add cauliflower and jicama; cover, reduce heat, and simmer for 5 minutes. Remove from heat; add cauliflower mixture, jalapeños, and zucchini to vegetable mixture. Let stand at room temperature 2 hours, stirring every 30 minutes. Discard spice bag; cover and store in refrigerator.
Note: Vegetable mixture can be stored up to 2 weeks in the refrigerator; serve at room temperature.