Mince garlic with a pinch of salt and add to a small bowl, along with vinegar. Add olives and parsley. Zest half of lemon into bowl (about 1 1/2 tsp.), then whisk in oil. Taste and season with salt.
Dunk frisée in water, leaves side down; then shake dry, cut off stem, and arrange leaves in a circle on a platter, stems facing in. (If frisée is sandy, cut stem off first and rinse leaves well before drying.) If using radicchio, tear leaves into 1-in. pieces.
Right before serving, drizzle frisée with vinaigrette and, using a razor-sharp grater, such as a Microplane, finely shred a layer of parmesan over salad.