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