Preheat oven to 400°F. Line a rimmed baking sheet with parchment paper and set aside.
In a large bowl, toss the halved potatoes with the olive oil, salt and pepper until well combined.
Spread the potatoes on the prepared baking sheet in one even layer and bake for 25 to 30 minutes until the edges are brown and crispy and the insides are tender when pierced with a fork or knife.
Meanwhile, add the arugula to the bowl you mixed the potatoes in. Toss the arugula making sure to scrape the sides and bottom of the bowl so the leftover oil, salt and pepper in the bowl is mixed with the arugula. Set aside.
Remove the potatoes from the oven. Sprinkle them with the minced garlic and chopped herbs. Toss well so the garlic and herbs are evenly distributed and then spread the potatoes back out into one even layer.
Put back in the oven for another 5 minutes to heat the garlic and herbs.
When potatoes are done place them in a bowl with the arugula. Squeeze the fresh lemon juice over everything and toss well. Add extra fresh cracked black pepper or a sprinkle of vegan parmesan, if desired.
Serve hot, room temperature, or even cold.