Place a pot of water with a steamer basket on your stove top over medium high heat. Meanwhile, half any large fingerling potatoes so they are all a similar size so they will cook evenly. Once the water comes to a boil, place the potatoes in the steamer basket and put a lid on. Cook until you can easily pierce through the potatoes with a fork. About 7-10 minutes depending on the size of your potatoes.
While the potatoes are cooking, make the vinaigrette in the bottom of the bowl you intend to serve the potato salad in. In the bottom of the bowl combine the shallot, vinegar, mustard, thyme, salt, pepper, and olive oil with a whisk.
When the potatoes are tender, remove them from the steamer and put them into the vinaigrette. Immediately put the green beans into the steamer just until tender. 2-3 minutes. Once tender, remove the green beans from the steamer and run under cold water for 10 seconds to stop the cooking. Then put them into the bowl with the potatoes and toss everything together. Top with parsley and serve immediately or put in the refrigerator to chill.