How to Make It
In a medium saucepan, melt 2 tablespoons of the butter. Stir in the Puy lentils; season lightly with salt and pepper. Add the chicken stock and bay leaf and bring to a boil. Simmer over low heat until the lentils are al dente, about 30 minutes.
Meanwhile, in a medium skillet, melt the remaining 2 tablespoons of butter. Add the diced carrot, zucchini, onion and celery. Season the vegetables with salt and pepper and cook over low heat, stirring, until just tender but not browned, about 10 minutes.
When the lentils are done, drain them over a medium bowl, reserving the cooking liquid. Discard the bay leaf. Return the lentils to the saucepan and pour in 1/2 cup of the reserved cooking liquid. Stir in the vegetables and season with salt and pepper.
Preheat the oven to 300°. Mix the flour and Parmesan cheese in a shallow bowl. Put the eggs in another shallow bowl and beat well. Season 4 of the veal slices with salt and pepper and dredge them in the Parmesan flour. Heat 1/2 cup of the olive oil in a large skillet. Quickly dip the floured veal into the egg mixture, then add the slices to the skillet and fry over moderately high heat until golden brown, about 2 minutes per side. Reduce the heat to moderate if the veal browns too quickly. Transfer the veal to a large rimmed baking sheet and keep warm in the oven. Repeat with the remaining 4 veal slices and keep warm in the oven while you finish the lentils.
Bring the lentils to a simmer. Remove from the heat and stir in the balsamic vinegar and the remaining 1 tablespoon of olive oil. Spoon the lentils onto plates, top with the veal, then sprinkle with the parsley and serve.