In a large bowl with enough lightly salted water to cover, place the cauliflower, pearl onions, red bell peppers, green bell peppers, celery and cucumbers. Soak 8 to 12 hours, or overnight. In a small bowl with enough lightly salted water to cover, place the carrots. Soak 8 to 12 hours, or overnight.
In a large saucepan, place the vegetable oil, vinegar, tomato paste and pickling spice. Bring the mixture to a boil. Drain and rinse the carrots, and place them in the mixture. Boil 10 minutes. Drain and rinse the vegetables in the cauliflower mixture. Place them into the saucepan. Cook 10 minutes, or until the cauliflower is tender but crisp. Stir black olives, green olives, mushrooms and tuna into the mixture.
Remove the mixture from heat. Discard the wrapped pickling spice. While still hot, transfer to sterile containers and refrigerate.