Preheat the oven to 425 degrees. Chop the potatoes into bite-size pieces (halves or quarters, depending on the size of the potatoes). Spread the potatoes on a baking sheet and drizzle with 2 tbsp of olive oil. Stir to make sure the potatoes are coated evenly, then season with salt + pepper to taste. Roast in the oven for 30 minutes, stirring halfway through, until the potatoes are crisp with golden edges.
Hard-boil the eggs
Place the eggs in a medium pot. Fill the pot with enough cold water so that the eggs are covered by 1 inch. Bring to a boil, then cover the pot and turn the heat off. Leave the pot on the element and allow the eggs to cook for 10-12 minutes. Afterwards, transfer the eggs to a bowl of ice water and allow to cool off for at least 10 minutes. Peel and chop the eggs once they are cool enough to handle. Set aside.
Make the dressing
In a food processor or blender, add all of the dressing ingredients and pulse until you get a chunky dressing. Taste and adjust the flavours if you'd like.
Transfer the slightly-cooled potatoes to a large mixing bowl. Pour the dressing over the potatoes and gently toss to coat (they will absorb more of the dressing when they are warm). Stir in the eggs, celery and red pepper flakes (if using). Garnish with more parsley and chives, and parmesan (if using). Serve warm or at room-temperature.