Place balsamic vinegar, lemon juice, anchovy paste, honey, and salt in a bowl, whisk to combine. Drizzle in olive oil, whisking the entire time. Taste and adjust.

Remove outer layers that are wilted and discard. Cut in half, place cut side down. Slice again, you'll get either 4 or 6 wedges from each head of radicchio.

Drizzle wedges with oil, salt, and pepper. Heat the grill. When hot, place radicchio on top and cook until charred and wilted, about 1-2 minutes each side.

Pour balsamic vinaigrette on the cooked radicchio. Allow to rest for 20 minutes. Top with grated Grana Padano and fresh chives. Sprinkle sea salt, then enjoy.