Start by boiling some salted water in a pot. Add in the egg noodles and cook them until they're just al dente, stirring occasionally to prevent sticking. Ensure not to overcook, as mushy pasta is not desirable.
In a separate pot, drop the petite potatoes into salted boiling water. They are done when fork-tender, which typically takes about 10 minutes. This salted water will help enhance the flavor of the potatoes.
Throw the green beans into another pot of boiling water for a couple of minutes. You want them to retain a vibrant green color and a bit of crunch. After cooking, quickly transfer them to ice water to halt the cooking process.
In a small bowl, whisk together the olive oil, lemon juice, shallots, both mustards, kosher salt, and pepper to create a dressing that smells fresh and zesty. Make sure everything is well combined to avoid any surprise bites of mustard.
In a large bowl, gently combine the cooked noodles, potatoes, green beans, shredded chicken, tomatoes, olives, cucumber, bell pepper, and onion. You should see a colorful mix. Stir lightly to keep everything intact; avoid squashing the tomatoes or potatoes.
Pour the vinaigrette over the tossed salad and mix it again. The warm potatoes will absorb some dressing, enhancing the flavor. Be cautious not to use too much dressing to overpower the other ingredients.
Gently fold in the capers and quartered hard-boiled eggs, adding a nice briny flavor and creaminess. Mix carefully to avoid breaking the eggs too much.
Allow the salad to sit in the fridge for about 30 minutes. This time lets the flavors blend nicely. Taste again before serving, adjusting seasoning or adding more dressing if necessary.