Bring a saucepan of salted water to a boil. Add the potatoes and boil for 15 minutes, until tender when pierced with a fork. Drain, rinse with cold water, and cut each potato in half.
While the potatoes are cooking, make the pesto. Put the greens, olive oil, and salt in the bowl of a food processor. Pulse for a minute or so until well combined.
Add the pine nuts and 1 teaspoon of the lemon juice, and pulse a few more times until the nuts are incorporated. If you'd like a thinner pesto, add more olive oil in a slow, steady stream with the food processor running. Taste the pesto and add salt, lemon juice, and/or freshly ground black pepper if desired.
Preheat the broiler. Spread one tablespoon of the oil onto a large sheet pan and place it under the broiler to preheat for 2-3 minutes. Season the steak with salt and pepper on both sides.
When the pan is preheated, add the steak in the center and the potatoes and asparagus around the edges. Drizzle the remaining tablespoon of oil over the vegetables and season them with salt and pepper.
Place the pan under the broiler for five minutes, then turn the steak over and gently stir the vegetables. Return the pan to the oven for 5-10 more minutes, or until the steak is cooked to your liking.
Transfer the steak to a cutting board and rest for five minutes, then slice across the grain. Serve the steak and vegetables with dollops of pesto.