Preheat oven to 400 degrees F. Line two large baking sheets with parchment paper.
Combine the potatoes, carrots, 2 tablespoons olive oil, salt, and pepper in a large bowl and mix well. Spread evenly onto the prepared baking sheets, allowing for some space between each piece so the potatoes will get nice and crispy! Roast for about 20 minutes, then remove from the oven.
Stir together the asparagus, broccoli, and remaining tablespoon of oil in a large bowl, then spread evenly onto the sheets with the potatoes and carrots. Return to the oven for 20-25 minutes, until the asparagus and broccoli are tender.
Meanwhile, combine all dressing ingredients in a small bowl and whisk well until creamy.
Serve the veggies on a platter or in individual bowls with a generous drizzle of the dressing. Garnish with parsley for some freshness, and dig in!