Step 1Take the beef out of the fridge, rinse and pat very dry, then let stand at room temperature while you prepare the grill
Step 2Prepare a charcoal or gas grill for indirect heat grilling. If using a charcoal grill, heat the coals until hot and ashed over, then bank to one side. If using a gas grill, heat all the burners to high. (You’ll heat the whole gas grill first, then turn off burners before cooking for indirect grilling.)
Step 3While the grill heats, tie the beef at 1-inch intervals with butcher’s twine. Sprinkle very generously with salt. Combine the ancho, garlic and ½ cup oil in a small bowl, then brush a coating of the mix all over the beef. Toss the persimmons with the remaining 2 teaspoons oil in another bowl, then sprinkle lightly with salt.
Step 4If using a gas grill, turn off all but one burner. Put the beef on the cool side of the grill and the persimmons on the hot side; reserve their bowl. If using a charcoal grill, put the persimmons over the coals and the beef on the other side. Cover and adjust the knobs or vents to maintain a grill temperature of 300 to 325 degrees.
Step 5Grill the persimmons, turning once, until charred and softened, 10 to 12 minutes. Grill the beef, turning 3 to 4 times and brushing lightly with the oil mixture, until an instant-read thermometer inserted in the thickest part of the beef registers 108 degrees, 25 to 30 minutes.
Step 6Return the persimmons to the reserved bowl and toss with the butter to evenly coat. Add the kimchi with its juices and fold to mix well.
Step 7Transfer the beef to the hot part of the grill. Grill, turning to evenly char and basting with the oil mixture every 5 to 6 minutes, until browned and an instant-read thermometer inserted in the thickest part registers 120 degrees, 15 to 20 minutes. Transfer to a cutting board and let rest for 15 minutes. Cut the beef into slices and serve with the persimmon kimchi.