Place potatoes in a large pot and cover with water. Bring to a boil, then cover and reduce heat to low. Allow them to steam/simmer for 15-20 minutes, or until fork tender.
Meanwhile, make the salad dressing by combining all dressing ingredients into a jar with a lid or in a small bowl. Shake or whisk to combine, adjusting seasonings to taste. Set aside.
When potatoes are cooked, remove them from the water using a slotted spoon. Place them in a clean bowl or cutting board to let them cool slightly.
Using the same pot of water, turn the heat up to high to return to a boil. You may need to add in some fresh water if it's looking a little low!
Once boiling, place the green beans into the pot and blanch them for 3-5 minutes. You want them to be tender enough to eat, but still bright green with a good crunch.
While the green beans are blanching, prepare an ice bath by placing ice cubes and cold water into a large bowl. Using your slotted spoon, transfer the green beans to the ice bath for 1-2 minutes to stop the cooking process.
Drain green beans and pat dry. Cut them into halves or thirds (depending on size) to make more bite-sized pieces.
Similarly, cut the cooked potatoes in halves or quarters depending on your desired size. If using pee-wee potatoes, you can add them to the salad whole.
In a large serving or mixing bowl, combine green beans and potatoes with arugula and goat cheese. Toss in dressing + serve!
