Pat your picanha steak down with paper towels. Flip the steak over so that the thick layer of fat is down against a cutting board. Use a sharp knife to trim away the steaks silverskin. Season the steak all over with Salt Pepper + Three Chile. Set the steak aside at room temperature for 1 hour
Set your grill or smoker for indirect heat at 225 º F . Smoke the picanha steak for 75 to 90 minutes or until the internal temperature reaches 120ºF.
While the steak cooks make the chimichurri by combining the parsley, oregano, garlic, red pepper, and vinegars in a mortar and pestle. Work this mixture into a thick paste and add a heavy pinch of kosher salt and oil and combine until you have a thick but chunky sauce. A small food processor works for this too — just combine the ingredients with a few short pulses.
Shape the burger meat into four 1/2 pound patties, squaring up the sides and making a shallow indent in one side. Season generously with kosher salt.
Remove the picanha steak from the grill to a baking sheet to rest. While it rests grill the burgers. Crank the heat on the grill to medium high and. Grill the burgers over direct heat for about 12 minutes total, flipping every 3 to 4 minutes.
Once again crank up the heat on the grill, aiming for about 500 degrees F. Return the steak to the grill and sear, turning every few minutes to prevent flare ups from that juicy fat cap. When the steak is darkly seared and reaches an internal temp of 130 degrees F, remove it from the grill to rest for 10 minutes.
While the steak rests, heat two cast iron skillet on the still hot grill and add the cheese slices to melt and crisp, this takes about 3 minutes.
Finally toast the buns and build the burger. Slice the steak and build the burgers – lettuce, burger patty, cheese skirt, steak slices, chimichurri.