• Coarsely chop the prosciutto.
• Cut the mushrooms into quarters.

In a large frying pan over medium-high heat, warm 1 teaspoon oil until hot but not smoking. Add the prosciutto and mushrooms and cook, stirring occasionally, until the prosciutto is crisp and the mushrooms are lightly browned, 6 to 8 minutes. Transfer to a paper-towel-lined plate. Do not clean the pan.

• Pat the chicken dry with a paper towel; season generously with salt and pepper.

In the same pan used for the prosciutto and mushrooms, if dry, add 1 to 2 teaspoons oil. Warm over medium heat until the fat is hot but not smoking. Add the chicken and cook, turning once, until lightly browned and cooked through, 3 to 5 minutes per side. Transfer to a plate. Do not clean the pan.
While the chicken cooks, prepare the remaining ingredients.

• Cut the nectarines in half and remove the pits; cut the fruit into ½-inch-thick wedges.
• Strip the parsley leaves from the stems; divide the leaves into two equal portions, one for the salad and one for garnish.

In the same pan used for the chicken, add the house dressing and cook over medium-low heat, scraping up any browned bits from the bottom of the pan, until warmed through, about 1 minute. Remove from the heat.
In a medium bowl, combine the arugula, nectarines, prosciutto, mushrooms, and half the parsley with as much dressing as you like and toss to coat; season to taste with salt and pepper.

Divide half the salad among individual plates. Top with the chicken and the remaining salad. Crumble the ricotta salata on top and drizzle with as much of the remaining dressing as you like. Garnish with the remaining parsley and serve.