Preheat the oven to Hi-Broil and grease a broiling pan with baking spray.
Place the steak in shallow bowl and season generously with salt & pepper. Add the balsamic vinegar, brown sugar and minced garlic and turn the steaks over a few times to coat. (The steaks can marinate like this for 1 hour up to overnight if you have the extra time. Otherwise, you can cook them immediately too).
Broil the steak for 10-12 minutes until medium-rare. Remove from the oven and let sit.
While the steak rests, turn the oven to 400 degrees, grease a baking sheet and place the portobello caps on the sheet. Drizzle with the olive oil and season with salt & pepper.
Bake the portobellos for 10 minutes until they start to shrink and expel their water.
While the mushrooms cook, slice the steak into thin strips.
Remove the mushrooms from the oven, drain the water from the caps and set aside.
For the Pistachio Pesto
Combine the basil, pistachios, parmesan, garlic, lemon juice and salt & pepper in a food processor.
Process and drizzle the olive oil in with the processor running. Scrape down the sides a few times until creamy.
To Assemble
Place a handful of arugula on top of each mushroom cap.
Top with sliced steak and drizzle the pesto over the top.