Step 1In a large saucepan, bring the salted water to a boil. Add the potatoes and cook until just soft, about 3 to 5 minutes, or longer depending on the size of the potatoes. Drain into a colander and let dry on paper towels.
Step 2While the potatoes are boiling, bring a small pot of water to a boil. Cook the green beans until just done but still crisp, about 4 to 5 minutes. Drain immediately and rinse in cold water to stop cooking. Drain and pat dry. Set aside on a small plate.
Step 3Light an outdoor grill or use a stove top grill pan. Cut the cooked potatoes in half or, if they are tiny, leave whole. Spray the cut side with olive oil. Grill, cut side down, until grill marks appear.
Step 4While the potatoes are grilling, mix the garlic, mustard, vinegar, parsley and mint in a small bowl. Slowly whisk in the olive oil. When the potatoes are grilled and still hot, toss them in the olive oil mixture and season with salt and pepper to taste. Add the green beans. Serve at room temperature.