Add potatoes to a medium pot and cover with water. Season water liberally with kosher salt (about 1 to 2 tablespoons) and bring to a boil.
While potatoes are cooking, wash green beans and trim off rough ends.
Once potatoes come to a boil, cook for about 8 minutes. Pierce potatoes with a fork to check for doneness. When potatoes are easily pierced, but still slightly firm, add green beans to the pot. Cook for 5 more minutes, until green beans are still crisp and potatoes are just cooked through.
Drain pot into a colander and rinse to stop cooking. Let potatoes and green beans cool a bit, while preparing other ingredients.
Dice ¼ cup red onion, slice celery into thin half-moon pieces and dice hard-boiled eggs.
For the dressing: Zest lemon and squeeze juice into a jar. Add in 3 tablespoons fresh, chopped dill and 1 tablespoon Dijon mustard. Add kosher salt (about 1 teaspoon) and cracked black pepper (about ¼ to ½ teaspoon). Drizzle in olive oil, add lid and shake vigorously until dressing is well combined.
Quarter cooked potatoes and cut green beans into 2-inch pieces. Add to a bowl with red onion, celery and hard-boiled eggs. Pour on dressing and stir to combine.
Taste, adjust seasoning and serve at room temperature with extra fresh dill sprinkled on top. Store leftover salad in the refrigerator in an air-tight container for up to 3 days.