Toss potatoes in olive oil and season with salt and pepper and grated lemon zest. Arrange, not overlapping, on a shallow baking sheet and bake until golden, about 30-35 minutes.
Add the asparagus and toss to coat. Return to oven until potatoes and crispy and asparagus is cooked, about eight-10 minutes more. Remove and sprinkle with chives and parsley.
Serve family style on a large platter or board with chicken drizzled with Romesco sauce.