Prepare the grill for direct and indirect grilling over a hot fire with an indirect grilling temperature of 500ºF.
Clean, dry and trim all the mushrooms. Spread them out in a baking pan or shallow dish. Drizzle generously with olive oil to coat the mushrooms and then season liberally with salt and pepper. Toss the mushrooms to coat them evenly and add more oil and seasoning as needed.
Lightly coat the tomahawk chops with olive oil and then season generously with salt and pepper.
Transfer the mushrooms from the pan onto the direct grilling zone of the grill. If you have a Kalamazoo laser-cut vegetable pattern grilling surface, use it for the mushrooms to keep them from falling through the grate. If not, use a pre-heated perforated grill pan. Cook the mushrooms until well-browned and most of the moisture has been removed, about 5 minutes for the shitakes and 10 minutes for the others. Remove all the mushrooms from the grill. Return them to the seasoning dish and reserve.
Place the tomahawk chops onto the direct grilling zone and brown on both sides (between 2 and 5 minutes on each side depending on the temperature of the direct grilling zone). Once nicely marked, transfer the chops to the indirect zone. Roast at 500ºF for 20 minutes, or until the internal temperature measures 155ºF. Remove the chops from the grill to rest. They will continue to climb in temperature to the desired 165ºF.
While the chops are roasting in the indirect grilling zone, prepare the chimichuri. Combine all the ingredients in a blender or food processor and process until smooth and thoroughly combined. Test for taste, adding salt, vinegar and chiles as needed.
If you are using the optional garlic scapes, lightly coat them with olive oil and season them with salt. Grill them in the direct zone until marked and tender, about 4 minutes.
Return the reserved mushrooms to the grill to reheat for about 1 minute.
For plating, put down a smear or squirt of chimichuri on the side of the plate. Place the mushrooms and garlic scapes on top of the sauce. Place the chop next to them on the clean portion of the plate.