For the gremolata, combine the lemon zest on a cutting board with the anchovy, parsley and garlic. Reserve.
Bring a pot of water to a boil for the pasta. Once boiling, salt the water and cook the pasta to al dente.
Meanwhile, season the chicken with salt and pepper on both sides then dredge in flour to coat. Beat the eggs in a shallow dish with splash of water. Dip both sides of the chicken in the eggs.
Heat 3 tablespoons EVOO and 2 tablespoons butter in a large skillet over medium to medium-high heat. Cook the chicken in two batches, 2 minutes on each side. Remove to a warm platter and reserve.
To the pan, add the wine, stock and lemon juice and reduce while the pasta cooks. Drain the pasta, then add the remaining 2 tablespoons butter to the sauce and melt. Douse the chicken in the sauce, then transfer it back to the platter. Add half of the gremolata to the sauce, then add the pasta, greens and basil and toss for 1-2 minutes.
Serve the pasta on large plates with the chicken alongside, garnished with the remaining gremolata.