In a small saucepan, stir until combined: 1 cup vinegar, olive oil, tomato paste, salt and pepper. Bring to a simmer. Remove from heat and let cool.
Breakdown cauliflower into small flowerettes and put into a large pot with sliced carrots. Cover with 4 cups water and add remaining 1 cup vinegar. Bring to a boil and cook just until al dente, 3-5 minutes. Immediately drain into strainer and let cool.
In a large glass bowl mix together undrained onions, pimentos and green olives. Add tomato sauce, dill pickles, tuna, black olives and cooked cauliflower and carrots.