1. For Roasted Pears: Adjust oven rack to lower-middle position, place baking sheet or broiler pan bottom on rack, and heat oven to 500 degrees.
2. Peel and halve each pear lengthwise. With paring knife or melon baller, remove core. Set each half cut-side down and slice lengthwise into fifths.
3. Toss pears with butter; add sugar and toss again to combine. Spread pears in single layer on preheated baking sheet, making sure each slice lies flat on surface. Roast until browned on bottom, about 10 minutes. Flip each slice and roast until tender and deep golden brown, about 5 minutes longer. Let pears cool while preparing salad.
4. For Salad: Whisk together oil, vinegar, salt, and pepper to taste in small bowl.
5. Combine arugula, pears, and Parmesan in large serving bowl. Add vinaigrette and toss gently to combine; sprinkle with chopped walnuts. Serve immediately.