1. Preheat oven to 450°.
2. Combine first 3 ingredients in a medium bowl; let stand 5 minutes or until bubbly. Stir in 4 teaspoons oil. Weigh or lightly spoon flour into a dry measuring cup and spoons; level with a knife. Add flour, 1/4 teaspoon salt, and pepper to yeast mixture, stirring until a soft dough forms. Turn dough out onto a lightly floured surface; knead until smooth and elastic (dough will be soft and tacky).
3. Place dough in a large bowl coated with cooking spray, turning to coat top. Cover and let rise in a warm place (85°), free from drafts, 45 minutes or until doubled in size. Punch dough down; cover and let rest 5 minutes.
4. Coat an 11 x 7-inch glass or ceramic baking dish with 2 teaspoons oil. Press dough into pan; cover and let rise 30 minutes or until puffy. Sprinkle dough with 1/4 teaspoon salt, walnuts, onion, prosciutto, and thyme. Bake at 450° for 18 minutes or until crust is golden and edges are crisp.
5. Place arugula in a bowl; drizzle with remaining 1 tablespoon oil and lemon juice, tossing to coat. Turn bread out onto a clean work surface, and slice crosswise into 4 rectangles. Top each rectangle with about 1/2 cup arugula mixture and 1 tablespoon shaved Parmesan cheese; sprinkle evenly with remaining 1/8 teaspoon salt.