1. In a medium saucepan over medium heat, heat 2 tablespoons of the olive oil and sweat the onion and garlic until tender, 5 to 7 minutes. Add the peppercorns and fennel seeds, and cook for 2 minutes. Add the white wine and remaining ¾ cup olive oil and simmer for 20 minutes.

2. Fill a bowl with water and add 2 tablespoons of the lemon juice. Cut off artichoke stems. Remove the outermost leaves by rotating the artichoke against the blade of a sharp knife. Trim off any leaves still attached to the bottoms. Cut the top third off each artichoke and discard. As you finish each artichoke, place immediately in the water bath. The citric acid will help retard discoloration (oxidation).

3. After the olive oil mixture has simmered for 20 minutes, strain it into a clean saucepan, discard spices, and return liquid to medium heat. Add the artichokes and cook, uncovered, stirring occasionally, until the artichokes are completely tender, 30 to 40 minutes. Transfer artichokes to a bowl. Cover bowl with plastic and refrigerate until ready to compose the salad.

4. Strain 1/2 cup artichoke cooking liquid into a measuring glass. Discard the rest. To this whisk in remaining 2 tablespoons lemon juice a little at a time. Taste, and season with salt and pepper. Add more lemon juice if necessary: vinaigrette should be well balanced and not too acidic.

5. Toss arugula with half the vinaigrette and plate. Drape pieces of ham over greens. Slice each artichoke in half and scatter pieces over greens and meat. Finish salads with shavings of cheese and vinaigrette.