Brush each prosciutto slice on 1 side lightly with some of oil.
Heat heavy large nonstick skillet over medium-high heat. Add 2 slices prosciutto, oiled side down. Cook until bottom is lightly browned, about 3 minutes. Turn prosciutto over and cook until bottom is browned, flattening with spatula, about 1 minute longer.
Using tongs, transfer prosciutto to paper towels to crisp.
Repeat with remaining 2 slices prosciutto. Reserve skillet.
Place greens and basil in large bowl.
Sprinkle scallops with salt and pepper; dust lightly with flour. Heat remaining oil in reserved skillet over medium-high heat. Add scallops and cook until brown and just opaque in center, about 3 minutes per side. Transfer to plate.
Add lemon juice and lemon peel to drippings in skillet. Bring to boil, scraping up any browned bits. Pour pan juices over greens and toss to coat. Season to taste with salt and pepper.
Divide salad among 4 plates and top with scallops. Garnish with prosciutto and serve.