Massage ¾ of the Pesto evenly onto both sides of the steaks and marinate them for 1 to 6 hours.
Preheat the grill to high, about 400°F.
Scrub the potatoes and sprinkle with a little salt. Bake them on the grill as it preheats, for about 35 to 55 minutes – depending on their size.
When they’re done, cut the tops off the potatoes, and carefully scoop out the flesh, leaving the skin intact. They’re still going to be hot, use oven mitts. Put the scooped out potatoes into a bowl and mash them with a fork, adding the butter and remaining pesto. (NOT the stuff that the steaks marinated in!) Season with salt and pepper to taste.
Turn off half of the burners on the grill, leaving one side on high. Put the mashed potatoes with pesto back into the potato shells and grill bake them on the top rack of the grill, over the “off” side, while you prepare the rest of the meal.
Put the asparagus on the top rack to grill with the potatoes, when you pull out the steaks to come to room temperature for 30 minutes before grilling.
Grill the steaks for 6 minutes per side, flipping once, until the touch test tells you they are done to your liking. Remember not to pierce the steak or smoosh it!
When the steaks are done, pull them off the grill and serve them with the potatoes and grilled asparagus.