Direction

1. Preheat an outdoor grill to medium heat (350 to 375 degrees F (175 to 190 degrees C)). Remove any wilted outer leaves from radicchio, then halve the head lengthwise through the core.
2. Brush cut sides of radicchio, avocados, and lemon with 1 tablespoon oil; arrange, cut sides down, along with the whole jalapeño, on grill grate. Cover grill. Grill radicchio, turning halfway through, until charred, 2 to 3 minutes. Grill avocados and lemon until cut sides are charred, 3 to 4 minutes. Grill jalapeño, turning to char on all sides, about 8 minutes.
3. When cool enough to handle, core and roughly chop radicchio and avocado; transfer to a serving bowl. Stem and (if desired) seed jalapeño.
4. For zhug, blend jalapeño, juice of grilled lemon, parsley, cilantro, garlic, coriander, salt, and remaining 4 tablespoons oil in a blender or food processor until smooth.
5. Add lettuce, Parmesan, and zhug to radicchio and avocado mixture; toss to coat. Serve immediately.