Preheat oven to 425°F (220°C). Boil the potatoes in salted water until fork-tender (about 15-20 minutes). Drain thoroughly and let them cool slightly (about 10 minutes).

Place the slightly cooled potatoes on a parchment-lined baking sheet. Using the bottom of a sturdy mug or a potato masher, gently but firmly smash each potato until it is about 1/2 inch thick. Be careful not to totally flatten them.

Drizzle the smashed potatoes evenly with 3 tablespoons of olive oil, then sprinkle with 1 teaspoon of salt and 1/2 teaspoon of pepper. Roast for 30-40 minutes, flipping carefully halfway through, until they are deeply golden brown and crispy on the edges.

While the potatoes roast, prepare the dressing. In a medium bowl, whisk together the mayonnaise, lemon juice, Dijon mustard, chopped dill, diced celery, and minced red onion. Season the dressing with additional salt and pepper to your preference.

Once the potatoes are beautifully crispy, remove them from the oven and let them cool for 5-10 minutes until they are warm, not piping hot.

Gently fold the warm, crispy potatoes into the prepared dressing. Toss lightly to coat, ensuring you maintain some of the potato's crispy texture. Serve immediately while still warm, or chill for at least one hour before serving cold.