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.