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