Quarter or half lthe potatoes: the goal is for all chunks to be roughly the same size. Boil a large pot of salted water and add the potatoes. Cook for 10 minutes.
While potatoes boil, trim the green beans. Add to the boiling potatoes and cook another 5-10 minutes, until the beans crisp tender and the potatoes fall apart when stabbed with a fork.
Meanwhile, heat 2 tbsp of olive oil in a large skillet on medium-high heat and put in the salmon skin side down. Cook 4-5 minutes, depending on the thickness of the fillet and flip, cooking 3-4 minutes more.
Beat together remaining oil, mustard, lemon, parsley, salt and pepper in a bowl.
Plate the salmon, potatoes and green beans, then pour the vinaigrette over everything.