Halve each artichoke heart lengthwise.
Thinly slice the hearts, tossing with 1 1/2 teaspoons lemon juice as you slice (to avoid discoloration).
Arrange on a platter, top with Parmesan, and drizzle with olive oil and remaining lemon juice. Season with 1/2 teaspoon salt and 1/4 teaspoon pepper to taste.
Sprinkle nuts and parsley over the top, and serve immediately.