Heat the grill to maximum temperature.
Cut the pointed cabbage lengthwise, then do it again. You should have 4 even pieces.
Place the fat in a small dish large enough to fit a quarter of the pointed cabbage.
Add salt, pepper, and cayenne pepper. Be generous with the seasoning, it should be well-distributed. Use a spoon or fork to mix.
Dip a piece of pointed cabbage in the fat on both cut sides.
Place it directly on the grill and repeat with the remaining pieces.
Grill for 5 minutes on each cut side.
Brush the outside with the remaining fat.
Grill the outside of the pointed cabbage for 3 minutes. At the same time, grill a halved lemon, cut side down.
Squeeze the grilled lemon juice over the cabbage pieces before serving.