Toast the walnuts: Toast the walnut halves in a dry skillet over medium heat, shaking often, until golden and fragrant — about 3–4 minutes. Tip onto a plate to cool slightly.
Pound the dressing base: Pound the toasted walnuts, garlic clove, and lemon zest in a mortar and pestle until coarsely crushed — rough, crumbly pieces, not powder. (Alternative: bash the walnuts in a freezer bag with a rolling pin, then mash the garlic with the flat of a knife and stir together.)
Finish the dressing: Stir the lemon juice, olive oil, grated Parmesan, salt, and pepper into the crushed walnut mixture until just combined. Keep it rough and chunky, not smooth. Adjust lemon and salt to taste.
Build the leaves: Combine the arugula, sliced endive, and radicchio in a large serving bowl.
Toss and serve: Pour the dressing over the leaves and toss gently but thoroughly. Scatter the shaved Parmesan curls over the top and serve immediately.