Add the potatoes to a 6-quart pot and pour in enough water to cover by two inches. Season with a teaspoon or two of salt and ½ teaspoon black pepper. Bring to a boil over medium heat and let cook at a good simmer, not a rolling boil, for about 10 minutes or until the potatoes are nearly, but not totally tender. Meanwhile, heat a stove top grill pan over medium high heat.
Place a colander on top of a bowl (make sure it sits steadily) and carefully fish out the potatoes with a spider or slotted spoon into the colander to drain for 2 minutes. Shake the colander to remove excess water and dump the water from the bowl into the sink. Tip the potatoes into the now water-free bowl; drizzle with olive oil and sprinkle with salt and pepper.
Turn the flame up under the pot of water until it’s boiling and add the green beans. Cook until they are just barely done, which will depend on the age and size of the beans. Mine took about 5 or 6 minutes. Drain in a colander in the sink and pat dry with paper towels.
As the green beans cook, pour the potatoes out onto the hot grill pan and grill for 3 minutes or so or until dark grill marks appear. Using tongs, turn potatoes and let the other side brown, cooking until the potatoes are tender. Remove potatoes to a large mixing bowl.
Add the cooked green beans to the potatoes in the bowl. Drizzle with olive oil and sprinkle with salt and pepper; stir carefully. Tip in the minced red onions, diced sweet peppers, and the minced tarragon; stir again. Drizzle with all but a tablespoon of the Tarragon Vinaigrette and toss gently until all of the vegetables are well-coated. Taste and adjust seasonings.
Turn salad out onto a platter or into a bowl and garnish with diced tomatoes and a little more minced tarragon. Drizzle the reserved tablespoon of vinaigrette evenly over all. Serve warm, at room temperature, or cold. (If you’re making the salad ahead and storing it in the fridge, you’ll need to add extra olive oil and vinegar or more vinaigrette at serving time as the vegetables will have absorbed the vinaigrette.)
*If you have no fresh tarragon, you can substitute 1 tablespoon dry and, if available, two tablespoons of fresh parsley, minced.