Combine vinegar, honey and saffron in a small pot. Bring to a boil over high heat; immediately remove from the heat and let sit until cooled to room temperature. Combine mayonnaise and garlic with saffron mixture in medium mixing bowl and season to taste with salt and pepper.
Cook potatoes in large pot of boiling, salted water until tender. Drain and slice into 1/2-inch thick rounds. Place in large serving bowl and immediately fold in mayonnaise mixture, tomatoes, onion, thyme and parsley. Season to taste with salt and pepper.