Cover the potatoes with water in a 6-quart pot; season with a teaspoon kosher salt and half-teaspoon fresh ground black pepper. Cover and bring to a rolling boil; turn down so that potatoes are simmering gently and let cook uncovered 10 minutes or until nearly tender. Add zucchini, broccoli, and cauliflower and let cook another 5 minutes. Drain in a colander in the sink and carefully turn vegetables out into a very large cotton towel, gently gathering the towel around the potato mixture to dry everything a bit. You can also blot them with paper towels if you prefer.
Light grill and heat to high or preheat stovetop grill pan. Tip vegetables into a large bowl and drizzle with 2 tablespoons extra virgin olive oil. Sprinkle on another ½ teaspoon each kosher salt and fresh ground pepper over all. Grill potatoes for 2-3 minutes, cut side down, or until dark grill marks appear. Turn potatoes over and add other vegetables and grill for another minute or two, turning as needed, until everything is fork-tender. You may need to do this in two shifts if you have a small grill or grill pan.
Return potatoes, zucchini, broccoli, and cauliflower back into the large bowl and sprinkle with a pinch of salt and pepper. Make vinaigrette: In a small bowl, whisk together 2 tablespoons red wine vinegar with a tablespoon of Dijon-style mustard, another pinch each salt and pepper, along with a dash or two of hot sauce—or to taste. Whisk in 4 tablespoons olive oil. Drizzle half of the vinaigrette over the grilled vegetables while they are hot and gently stir until totally coated.
Stir in the onions, bell pepper, lemon zest, parsley, tarragon, and dill. Drizzle with the remainder of the vinaigrette, stirring again gently until well combined. Taste, adjusting seasonings as necessary. Serve warm or at room temperature. May store in the refrigerator up to 3 days, perhaps adding a little olive oil and vinegar to freshen the salad up.