Piccata is a classic Milanese veal preparation, where the veal is quickly sauteed and served with a pan sauce made of stock, lemon juice, capers, and parsley. We've added wine to our sauce, which gives the dish extra zest. If you can't find veal in your area, use thinly pounded boneless, skinless chicken breasts instead. For this preparation, thin veal cutlets are pounded to 1/4-inch thickness for a quick cooking time that preserves the meat's natural tenderness and flavor.
Bring a large pot of salted water to the boil. Add the pasta and cook, stirring to separate the strands of pasta, until just al dente, about 4 minutes. Drain in a colander and return to the pot. Add 2 tablespoons of extra-virgin olive oil, 1/2 teaspoon of the salt, 1/4 teaspoon of the pepper, 2 tablespoons of the parsley, the basil, and the cheese and toss to coat. Cover to keep warm.
Meanwhile, combine the flour with 1 teaspoon of the salt and 1 teaspoon of the black pepper in a shallow bowl.
Lightly season both sides of each medallion with 1/8 teaspoon of the remaining salt and a pinch of the remaining pepper. One at a time, dredge the medallions in the seasoned flour, shaking to remove any excess.
Heat the remaining 2 tablespoons of oil and melt 1 tablespoon of the butter in a large skillet or saute pan over medium-high heat. Add the medallions in batches and cook until golden brown and just cooked through, 1 to 1 1/2 minutes per side. Drain on paper towels and set aside.
Add the wine to the juices remaining in the pan and bring to a boil, stirring to deglaze the pan, and cook until the wine is reduced by half, 2 to 3 minutes. Add the chicken stock, lemon juice, capers, and garlic and return to a boil, stirring, until the mixture is thickened, about 4 minutes. Stir in the remaining 2 tablespoons butter and 1 tablespoon of the parsley. When the butter is melted, return all of the veal medallions to the pan and cook until heated through, about 1 minute.
To serve, divide the pasta among 4 large plates and arrange 2 veal medallions on each plate. Spoon the sauce over the veal and garnish each serving with 1/4 teaspoon of the remaining parsley. Serve immediately.