Papardelle with Arugula and Prosciutto

INGREDIENTS

• 1/2 pound pappardelle or fettuccine
• Kosher salt
• 2 tablespoons olive oil
• 2 tablespoons unsalted butter
• 2 leeks, white and pale greens only, halved lengthwise, thinly sliced crosswise
• 1/4 cup chopped fresh chives
• 2 teaspoons finely grated lemon zest plus more for serving
• 1 bunch arugula, thick stems trimmed, leaves torn (about 4 cups)
• 1/3 cup finely grated Parmesan plus more for serving
• Freshly ground black pepper
• 3 ounces prosciutto, torn into 1" pieces