Bring 5-6 cups of water to a boil over high heat. Place potatoes and 1 1/2 teaspoons of salt, reduce the water to medium-low and simmer until the potatoes are full cooked or tender for about 15 minutes.
Whisk oil, dijon mustard, vinegar, fresh lemon juice, a pinch of pepper, a pinch of salt in large bowl. Add chopped anchovies, garlic, shallots, give it a stir and set aside.
Drain potatoes and green beans thoroughly, drizzle some vinegar and gently toss. Let it cool for 15 minutes.
Add chopped tomatoes, fresh parsley, and green peas. Drizzle with generous amount of anchovy vinaigrette dressing. Serve immediately and enjoy.