Melt a stick of butter in a small saucepan over medium heat and cook for 3 to 4 minutes until foamy. Remove from the heat and allow the milk solids to settle; slowly pour off the clarified butter and wipe out the milk solids.
Soak the meat in the milk in a shallow dish for a few minutes, then drain. Season the meat with salt and pepper, then coat with the flour, the eggs, the breadcrumbs mixed with the sage or fennel, the cheese and grated nutmeg.
Bring a pot of water to a boil, salt it, add the gnocchi and cook through; drain.
While the pasta is working, heat a few tablespoons each of EVOO and clarified butter in each of 2 large skillets over medium to medium-high heat. Add the cutlets to each skillet and cook until deeply golden on each side, 6 to 7 minutes total. Keep the cutlets warm in a low oven or on a warm platter. Wipe out one of the skillets and return to the stove. Brown the remaining 2 tablespoons butter for 4 minutes. Add the gnocchi, coat in the butter and season with salt and pepper. Garnish with the parsley.
Serve the cutlets with the lemon quarters, gnocchi and watercress (or arugula).