Preheat your oven to 425°F (220°C). Line a large baking sheet with parchment paper.

Toss the quartered potatoes with 3 Tbsp of olive oil, kosher salt, and pepper directly on the baking sheet. Spread them into a single layer to ensure even roasting.

Roast the potatoes for 35 to 45 minutes, flipping halfway through, until they are deeply golden brown and tender on the inside with crispy edges.

While the potatoes roast, prepare the vinaigrette: Whisk together the Dijon mustard, apple cider vinegar, 4 Tbsp olive oil, minced shallot, salt, and pepper in a small bowl until emulsified.

Remove the roasted potatoes from the oven and immediately transfer them to a large mixing bowl while still warm. This helps them absorb the dressing better.

Pour about half of the vinaigrette over the warm potatoes and gently toss. Let sit for 5 minutes.

Add the diced celery, chopped parsley, chives, and chopped egg (if using) to the bowl. Pour the remaining vinaigrette over the mixture and gently fold everything together until just combined. Taste and adjust seasoning if necessary.

Serve immediately while warm, or allow to cool to room temperature before serving.