Cut potatoes into 1-inch cubes and place in a large pot, then cover with cold salted water. Bring to a boil over high heat. While the potatoes cook, trim the green beans and cut into 2-inch pieces, then thinly slice the red onion and chop the scallions and fresh dill. Having everything prepped before the potatoes finish ensures you can work quickly once they're tender.
When the potatoes are just tender (about 12-15 minutes depending on size), add the prepared green beans to the same pot and boil for exactly 5 minutes. The beans should be bright green and tender-crisp, not soft. Drain both vegetables in a colander and let them sit for a minute to release excess moisture—this prevents a watery salad.
While the vegetables drain, whisk together the lemon juice, lemon zest, Dijon mustard, sea salt, and black pepper in a small bowl. Slowly drizzle in the olive oil while whisking constantly to emulsify the dressing. I find whisking by hand helps me feel when the vinaigrette comes together perfectly, creating a creamy texture rather than an oily one.
Transfer the warm drained potatoes and green beans to a large serving bowl. Add the sliced red onion and pour the vinaigrette over the vegetables while they're still warm—this allows them to absorb the dressing better. Gently toss everything together, then fold in the chopped scallions and fresh dill just before serving. I recommend adding the fresh herbs last so they stay vibrant and don't bruise from too much tossing.