For the artichokes: Preheat the oven to 350 degrees F.
To clean the artichokes, trim the outside green leaves until you reach the soft, yellow leaves. Cut the tops off. Trim off any hard stems. Slice the artichokes in half through the stems. Arrange the artichokes on a baking sheet in a single layer and toss with the oil, salt and pepper. Roast until tender, 25 to 30 minutes.
For the gremolata: Meanwhile, in a food processor, add the parsley and walnuts and pulse until the nuts are finely chopped. Add the mustard, salt, pepper, garlic and lemon zest and juice. With the motor running, slowly add the oil and process until smooth.
Toss the warm artichokes with the gremolata and serve hot.